JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank

done Plane Total Questions - 74

• question_answer1)
  The angle between the planes \[3x-4y+5z=0\] and \[2x-y-2z=5\] is [MP PET 1988]
  A)
             \[\frac{\pi }{3}\] done clear
  B)
             \[\frac{\pi }{2}\] done clear
  C)
             \[\frac{\pi }{6}\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer2)
  The equation of the plane which is parallel to y-axis and cuts off intercepts of length 2 and 3 from x-axis and z-axis is                
  A)
             \[3x+2z=1\] done clear
  B)
             \[3x+2z=6\] done clear
  C)
             \[2x+3z=6\] done clear
  D)
             \[3x+2z=0\] done clear
  View Solution play_arrow

• question_answer3)
  If a plane cuts off intercepts ?6, 3, 4 from the co-ordinate axes, then the length of the perpendicular from the origin to the plane is 
  A)
             \[\frac{1}{\sqrt{61}}\] done clear
  B)
             \[\frac{13}{\sqrt{61}}\] done clear
  C)
             \[\frac{12}{\sqrt{29}}\] done clear
  D)
             \[\frac{5}{\sqrt{41}}\] done clear
  View Solution play_arrow

• question_answer4)
  The equation of the plane which is parallel to xy-plane and cuts intercept of length 3 from the z-axis is
  A)
             \[x=3\] done clear
  B)
             \[y=3\] done clear
  C)
             \[z=3\] done clear
  D)
             \[x+y+z=3\] done clear
  View Solution play_arrow

• question_answer5)
  The equation of the plane which bisects the angle between the planes \[3x-6y+2z+5=0\] and \[4x-12y+3z-3=0\] which contains the origin is
  A)
             \[33x-13y+32z+45=0\] done clear
  B)
             \[x-3y+z-5=0\] done clear
  C)
             \[33x+13y+32z+45=0\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer6)
  The value of k for which the planes \[3x-6y-2z=7\] and \[2x+y-kz=5\] are perpendicular to each other, is                                                               [MP PET 1992]
  A)
             0 done clear
  B)
             1 done clear
  C)
             2 done clear
  D)
             3 done clear
  View Solution play_arrow

• question_answer7)
  The equation of the plane passing through the point  (?1, 3, 2) and perpendicular to each of the planes \[x+2y+3z=5\] and \[3x+3y+z=0\], is
  A)
             \[7x-8y+3z-25=0\] done clear
  B)
             \[7x-8y+3z+25=0\] done clear
  C)
             \[-7x+8y-3z+5=0\] done clear
  D)
             \[7x-8y-3z+5=0\] done clear
  View Solution play_arrow

• question_answer8)
  The distance between the planes \[x+2y+3z+7=0\] and \[2x+4y+6z+7=0\] is [MP PET 1991]
  A)
             \[\frac{\sqrt{7}}{2\sqrt{2}}\] done clear
  B)
             \[\frac{7}{2}\] done clear
  C)
             \[\frac{\sqrt{7}}{2}\] done clear
  D)
             \[\frac{7}{2\sqrt{2}}\] done clear
  View Solution play_arrow

• question_answer9)
  If a plane cuts off intercepts \[OA=a,OB=b,\] \[OC=c\] from the co-ordinate axes, then the area of the triangle \[ABC\]=
  A)
             \[\frac{1}{2}\sqrt{{{b}^{2}}{{c}^{2}}+{{c}^{2}}{{a}^{2}}+{{a}^{2}}{{b}^{2}}}\] done clear
  B)
             \[\frac{1}{2}(bc+ca+ab)\] done clear
  C)
             \[\frac{1}{2}abc\] done clear
  D)
   \[\frac{1}{2}\sqrt{{{(b-c)}^{2}}+{{(c-a)}^{2}}+{{(a-b)}^{2}}}\]                done clear
  View Solution play_arrow

• question_answer10)
  If the product of distances of the point (1, 1, 1) from the origin and the plane \[x-y+z+k=0\] be 5, then  k =
  A)
             ? 2 done clear
  B)
             ?3 done clear
  C)
             4 done clear
  D)
             7 done clear
  View Solution play_arrow

• question_answer11)
  The equation of the plane which is parallel to the plane \[x-2y+2z=5\] and whose distance from the point \[(1,\,2,\,3)\] is 1, is
  A)
             \[x-2y+2z=3\] done clear
  B)
             \[x-2y+2z+3=0\] done clear
  C)
             \[x-2y+2z=6\] done clear
  D)
             \[x-2y+2z+6=0\] done clear
  View Solution play_arrow

• question_answer12)
  The equation of the plane through (1, 2, 3) and parallel to the plane \[2x+3y-4z=0\]is [MP PET 1990]
  A)
             \[2x+3y+4z=4\] done clear
  B)
             \[2x+3y+4z+4=0\] done clear
  C)
             \[2x-3y+4z+4=0\] done clear
  D)
             \[2x+3y-4z+4=0\] done clear
  View Solution play_arrow

• question_answer13)
  Distance of the point (2,3,4) from the plane \[3x-6y+2z+11=0\]is [MP PET 1990, 96]
  A)
             1 done clear
  B)
             2 done clear
  C)
             3 done clear
  D)
             0 done clear
  View Solution play_arrow

• question_answer14)
  The equation of the plane containing the line of intersection of the planes \[2x-y=0\]and \[y-3z=0\]and perpendicular to the plane \[4x+5y-3z-8=0\]is
  A)
             \[28x-17y+9z=0\] done clear
  B)
             \[28x+17y+9z=0\] done clear
  C)
             \[28x-17y+9x=0\] done clear
  D)
             \[7x-3y+z=0\] done clear
  View Solution play_arrow

• question_answer15)
  A point moves in such a way that the sum of its distance from xy-plane and yz-plane remains equal to its distance from zx-plane. The locus of the point is
  A)
             \[x-y+z=2\] done clear
  B)
             \[x+y-z=0\] done clear
  C)
             \[x-y+z=0\] done clear
  D)
             \[x-y-z=2\] done clear
  View Solution play_arrow

• question_answer16)
  A point moves so that its distances from the points (3, 4, ?2) and (2, 3, ? 3) remains equal. The locus of the point is
  A)
             A line done clear
  B)
             A  plane whose normal is equally inclined to axes  done clear
  C)
             A plane which passes through the origin done clear
  D)
             A sphere done clear
  View Solution play_arrow

• question_answer17)
  The equation of the  perpendicular from the point  \[(\alpha ,\beta ,\gamma )\] to the plane \[ax+by+cz+d=0\]is [MP PET 2003]
  A)
             \[a(x-\alpha )+b(y-\beta )+c(z-\gamma )=0\] done clear
  B)
             \[\frac{x-\alpha }{a}=\frac{y-\beta }{b}=\frac{z-\gamma }{c}\] done clear
  C)
             \[a(x-\alpha )+b(y-\beta )+c(z-\gamma )=abc\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer18)
  The equation of yz-plane is [MP PET 1988]
  A)
             \[x=0\] done clear
  B)
             \[y=0\] done clear
  C)
             \[z=0\] done clear
  D)
             \[x+y+z=0\] done clear
  View Solution play_arrow

• question_answer19)
  The angle between the planes \[2x-y+z=6\] and \[x+y+2z=7\] is  [MP PET 1991, 98, 2000, 01, 03; RPET 2001]
  A)
             \[30{}^\circ \] done clear
  B)
             \[45{}^\circ \] done clear
  C)
             \[0{}^\circ \] done clear
  D)
             \[60{}^\circ \] done clear
  View Solution play_arrow

• question_answer20)
  The equation of the plane passing through the line of intersection of the planes \[x+y+z=1\] and \[2x+3y-z+4=0\]and parallel to x-axis is
  A)
             \[y-3z-6=0\] done clear
  B)
             \[y-3z+6=0\] done clear
  C)
             \[y-z-1=0\] done clear
  D)
             \[y-z+1=0\] done clear
  View Solution play_arrow

• question_answer21)
  The co-ordinates of the foot of the perpendicular drawn from the origin to a plane is (2, 4, ?3). The equation of the plane is
  A)
             \[2x-4y-3z=29\] done clear
  B)
             \[2x-4y+3z=29\] done clear
  C)
             \[2x+4y-3z=29\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer22)
  The equation of a plane which passes through (2, ?3, 1) and is normal to the line joining the points (3, 4, ?1) and (2, ?1, 5) is given by      [AI CBSE 1990; MP PET 1993]
  A)
             \[x+5y-6z+19=0\] done clear
  B)
             \[x-5y+6z-19=0\] done clear
  C)
             \[x+5y+6z+19=0\] done clear
  D)
             \[x-5y-6z-19=0\] done clear
  View Solution play_arrow

• question_answer23)
  The length and foot of the perpendicular from the point       (7, 14, 5) to the plane \[2x+4y-z=2,\]are [AISSE 1987]
  A)
             \[\sqrt{21},(1,\,2,\,8)\] done clear
  B)
             \[3\sqrt{21},(3,\,2,\,8)\] done clear
  C)
             \[21\sqrt{3},(1,\,2,\,8)\] done clear
  D)
             \[3\sqrt{21},(1,\,2,\,8)\] done clear
  View Solution play_arrow

• question_answer24)
  The equation of the plane passing through the intersection of the planes \[x+y+z=6\] and \[2x+3y+4z+5=0\] the point (1, 1, 1), is [AISSE 1983]
  A)
             \[20x+23y+26z-69=0\] done clear
  B)
             \[20x+23y+26z+69=0\] done clear
  C)
             \[23x+20y+26z-69=0\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer25)
  The equation of the plane through the three points (1, 1, 1), (1, ?1, 1) and (?7,?3,?5), is [AISSE 1984]
  A)
             \[3x-4z+1=0\] done clear
  B)
             \[3x-4y+1=0\] done clear
  C)
             \[3x+4y+1=0\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer26)
  The ratio in which the plane \[x-2y+3z=17\] divides the line joining the points (?2, 4, 7) and \[(3,-5,\,8)\]is [AISSE 1988]
  A)
             10 : 3 done clear
  B)
             3 : 1 done clear
  C)
              3 : 10 done clear
  D)
             10 : 1 done clear
  View Solution play_arrow

• question_answer27)
  Image point of \[(1,\,3,4)\] in the plane \[2x-y+z+3=0\] is
  A)
             (? 3, 5, 2) done clear
  B)
             (3, 5, ? 2) done clear
  C)
             (3, ? 5, 3) done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer28)
  Distance between parallel planes \[2x-2y+z+3=0\] and \[4x-4y+2z+5=0\] is [MP PET 1994, 95]
  A)
             \[\frac{2}{3}\] done clear
  B)
             \[\frac{1}{3}\] done clear
  C)
             \[\frac{1}{6}\] done clear
  D)
             2 done clear
  View Solution play_arrow

• question_answer29)
  If the given planes \[ax+by+cz+d=0\] and \[a'x+b'y+c'z+d'=0\] be mutually perpendicular, then            [MP PET 1994]
  A)
             \[\frac{a}{a'}=\frac{b}{b'}=\frac{c}{c'}\] done clear
  B)
             \[\frac{a}{a'}+\frac{b}{b'}+\frac{c}{c'}=0\] done clear
  C)
             \[aa\,'+\,bb\,'+\,cc\,'+\,dd\,'=0\] done clear
  D)
             \[aa\,'+\,bb\,'+\,cc\,'=0\] done clear
  View Solution play_arrow

• question_answer30)
  A point (x, y, z) moves parallel to xy?plane. Which of the three variables x, y, z remain fixed
  A)
             z done clear
  B)
             y done clear
  C)
             x done clear
  D)
             x and y done clear
  View Solution play_arrow

• question_answer31)
  The angle between two planes is equal to
  A)
             The angle between the tangents to them from any point done clear
  B)
             The angle between the normals to them from any point done clear
  C)
                     The angle between the lines parallel to the planes from any point              done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer32)
  In three dimensional space, the equation \[3y+4z=0\] represents
  A)
             A plane containing x-axis          done clear
  B)
             A plane containing y-axis done clear
  C)
             A plane containing z-axis          done clear
  D)
             A line with direction ratios 0, 3, 4 done clear
  View Solution play_arrow

• question_answer33)
  A plane meets the co-ordinate axes in \[A,B,C\] and \[(\alpha ,\beta ,\gamma )\] is the centered of the triangle \[ABC\]. Then  the equation of the plane is [MP PET 2004]
  A)
             \[\frac{x}{\alpha }+\frac{y}{\beta }+\frac{z}{\gamma }=3\] done clear
  B)
             \[\frac{x}{\alpha }+\frac{y}{\beta }+\frac{z}{\gamma }=1\] done clear
  C)
             \[\frac{3x}{\alpha }+\frac{3y}{\beta }+\frac{3z}{\gamma }=1\] done clear
  D)
             \[\alpha x+\beta y+\gamma z=1\] done clear
  View Solution play_arrow

• question_answer34)
  If the planes \[3x-2y+2z+17=0\]and \[4x+3y-kz=25\] are mutually perpendicular , then \[k=\] [MP PET 1995]
  A)
             3 done clear
  B)
             ? 3 done clear
  C)
             9 done clear
  D)
             ? 6 done clear
  View Solution play_arrow

• question_answer35)
  If O is the origin and A is the point (a, b, c) then the equation of the plane through A and at right angles to OA is                    [AMU 2005]
  A)
             \[a(x-a)-b(y-b)-c(z-c)=0\] done clear
  B)
             \[a(x+a)+b(y+b)+c(z+c)=0\] done clear
  C)
             \[a(x-a)+b(y-b)+c(z-c)=0\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer36)
  If from a point  \[P(a,b,c)\] perpendiculars \[PA\] and \[PB\]are drawn to yz and zx planes, then the equation of the plane \[OAB\] is
  A)
             \[bcx+cay+abz=0\] done clear
  B)
             \[bcx+cay-abz=0\] done clear
  C)
             \[bcx-cay+abz=0\] done clear
  D)
             \[-bcx+cay+abz=0\] done clear
  View Solution play_arrow

• question_answer37)
  The graph of the equation \[{{y}^{2}}+{{z}^{2}}=0\] in three dimensional space is
  A)
             x-axis done clear
  B)
             z-axis done clear
  C)
             y-axis done clear
  D)
             yz-plane done clear
  View Solution play_arrow

• question_answer38)
  A variable plane is at a constant distance p from the origin and meets the axes in A, B and C. The locus of the centroid of the tetrahedron \[OABC\] is
  A)
             \[{{x}^{-2}}+{{y}^{-2}}+{{z}^{-2}}=16{{p}^{-2}}\]                          done clear
  B)
             \[{{x}^{-2}}+{{y}^{-2}}+{{z}^{-2}}=16{{p}^{-1}}\] done clear
  C)
             \[{{x}^{-2}}+{{y}^{-2}}+{{z}^{-2}}=16\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer39)
  The plane \[ax+by+cz=1\]meets the co-ordinate axes in A, B and C. The centroid of the triangle is [CET 1992]
  A)
             \[(3a,3b,3c)\] done clear
  B)
             \[\left( \frac{a}{3},\frac{b}{3},\frac{c}{3} \right)\] done clear
  C)
             \[\left( \frac{3}{a},\frac{3}{b},\frac{3}{c} \right)\] done clear
  D)
             \[\left( \frac{1}{3a},\frac{1}{3b},\frac{1}{3c} \right)\] done clear
  View Solution play_arrow

• question_answer40)
  The equation of a plane which cuts equal intercepts of unit length on the axes, is [MP PET 1996]
  A)
             \[x+y+z=0\] done clear
  B)
             \[x+y+z=1\] done clear
  C)
             \[x+y-z=1\] done clear
  D)
             \[\frac{x}{a}+\frac{y}{a}+\frac{z}{a}=1\] done clear
  View Solution play_arrow

• question_answer41)
  The equation of the plane through (2, 3, 4) and parallel to the plane \[x+2y+4z=5\]is [MP PET 1996]
  A)
             \[x+2y+4z=10\] done clear
  B)
             \[x+2y+4z=3\] done clear
  C)
             \[x+y+2z=2\] done clear
  D)
             \[x+2y+4z=24\] done clear
  View Solution play_arrow

• question_answer42)
  The plane \[\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=3\]meets the co-ordinate axes in \[A,B,C\]. The centroid of the triangle ABC is    [DCE 2005]
  A)
             \[\left( \frac{a}{3},\frac{b}{3},\frac{c}{3} \right)\] done clear
  B)
             \[\left( \frac{3}{a},\frac{3}{b},\frac{3}{c} \right)\] done clear
  C)
             \[\left( \frac{1}{a},\frac{1}{b},\frac{1}{c} \right)\] done clear
  D)
             \[(a,b,c)\] done clear
  View Solution play_arrow

• question_answer43)
  The planes \[x=cy+bz,y=az+cx,z=bx+ay\]pass through one line, if
  A)
             \[a+b+c=0\] done clear
  B)
             \[a+b+c=1\] done clear
  C)
             \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=1\] done clear
  D)
             \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}+2abc=1\] done clear
  View Solution play_arrow

• question_answer44)
  If the length of perpendicular drawn from origin on a plane is 7 units and its direction ratios are ?3, 2, 6, then that plane is [MP PET 1998]
  A)
             \[-3x+2y+6z-7=0\] done clear
  B)
             \[-3x+2y+6z-49=0\] done clear
  C)
             \[3x-2y+6z+7=0\] done clear
  D)
             \[-3x+2y-6z-49=0\] done clear
  View Solution play_arrow

• question_answer45)
  If the plane \[x-3y+5z=d\]passes through the point (1,2,4), then the lengths of intercepts cut by it on the axes of x, y, z are respectively [MP PET 1998]
  A)
             15, ?5, 3 done clear
  B)
             1, ?5, 3 done clear
  C)
             ?15, 5, ?3 done clear
  D)
             1, ?6, 20 done clear
  View Solution play_arrow

• question_answer46)
  If the planes \[x+2y+kz=0\] and \[2x+y-2z=0\] are at right angles, then the value of k is [MP PET 1999]
  A)
             \[-\frac{1}{2}\] done clear
  B)
             \[\frac{1}{2}\] done clear
  C)
             ? 2 done clear
  D)
             2 done clear
  View Solution play_arrow

• question_answer47)
  If two planes intersect , then the shortest distance between the planes is [Kurukshetra CEE 1998]
  A)
             \[\cos \theta \] done clear
  B)
             \[\cos {{90}^{o}}\] done clear
  C)
             \[\sin {{90}^{o}}\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer48)
   The length of the perpendicular from the origin to the plane \[3x+4y+12z=52\]is [MP PET 2000; Pb. CET 2001]
  A)
             3 done clear
  B)
   ?4 done clear
  C)
             5 done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer49)
   If P be the point (2, 6, 3), then the equation of the  plane through P at right angle to OP, O being the origin, is    [MP PET 2000; Pb. CET 2001]
  A)
             \[2x+6y+3z=7\] done clear
  B)
             \[2x-6y+3z=7\] done clear
  C)
             \[2x+6y-3z=49\] done clear
  D)
             \[2x+6y+3z=49\] done clear
  View Solution play_arrow

• question_answer50)
  The distance of the point (2, 3, ? 5) from the plane \[x+2y-2z=9\]is [MP PET 2001]
  A)
             4 done clear
  B)
             3 done clear
  C)
             2 done clear
  D)
             1 done clear
  View Solution play_arrow

• question_answer51)
  The intercepts of the plane \[5x-3y+6z=60\]on the           co-ordinate axes are [Pb. CET 2000 ; MP PET 2001]
  A)
             \[(10,\,20,\,-10)\] done clear
  B)
             (10, ? 20, 12) done clear
  C)
             (12, ? 20, 10) done clear
  D)
             (12, 20, ? 10) done clear
  View Solution play_arrow

• question_answer52)
  The equation of a plane parallel to x- axis  is [DCE 2001]
  A)
             \[ax+by+cz+d=0\] done clear
  B)
             \[ax+by+d=0\] done clear
  C)
             \[by+cz+d=0\] done clear
  D)
             \[ax+cz+d=0\] done clear
  View Solution play_arrow

• question_answer53)
  The points \[A(-1,3,0)\], \[B\,(2,\,2,\,1)\] and \[C\,(1,\,1,\,3)\] determine a plane. The distance from the plane to the point \[D(5,\,7,8)\] is                                                               [AMU 2001]
  A)
             \[\sqrt{66}\] done clear
  B)
             \[\sqrt{71}\] done clear
  C)
             \[\sqrt{73}\] done clear
  D)
             \[\sqrt{76}\] done clear
  View Solution play_arrow

• question_answer54)
  In a three dimensional xyz space the equation \[{{x}^{2}}-5x+6=0\] represents [Orissa JEE 2002]
  A)
             Points done clear
  B)
             Plane done clear
  C)
             Curves done clear
  D)
             Pair of straight line done clear
  View Solution play_arrow

• question_answer55)
  The equations \[|x|=p,|y|=p,|z|=p\] in xyz space represent [Orissa JEE 2002]
  A)
             Cube done clear
  B)
             Rhombus done clear
  C)
             Sphere of radius p done clear
  D)
             Point (p, p, p) done clear
  View Solution play_arrow

• question_answer56)
  In the space the equation \[by+cz+d=0\] represents a plane perpendicular to the plane [EAMCET 2002]
  A)
             \[YOZ\] done clear
  B)
             \[Z=k\] done clear
  C)
             \[ZOX\] done clear
  D)
             \[XOY\] done clear
  View Solution play_arrow

• question_answer57)
  The equation of the plane through the point (1, 2, 3 ) and parallel to the plane \[x+2y+5z=0\]is      [DCE 2002]
  A)
             \[(x-1)+2(y-2)+5(z-3)=0\] done clear
  B)
             \[x+2y+5z=14\] done clear
  C)
             \[x+2y+5z=6\]                            done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer58)
  The equation of the plane passing through the intersection of the planes \[x+2y+3z+4=0\] and \[4x+3y+2z+1=0\] and the origin is [Kerala (Engg.) 2002]
  A)
             \[3x+2y+z+1=0\] done clear
  B)
             \[3x+2y+z=0\] done clear
  C)
             \[2x+3y+z=0\] done clear
  D)
             \[x+y+z=0\] done clear
  View Solution play_arrow

• question_answer59)
  The equation of the plane passing through  (2, 3, 4) and  parallel  to the plane \[5x-6y+7z=3\] [Kerala (Engg.) 2002]
  A)
             \[5x-6y+7z+20=0\] done clear
  B)
             \[5x-6y+7z-20=0\] done clear
  C)
             \[-5x+6y-7z+3=0\] done clear
  D)
             \[5x+6y+7z+3=0\] done clear
  View Solution play_arrow

• question_answer60)
  The distance of the plane \[6x-3y+2z-14=0\]from the origin is [MP PET 2003]
  A)
             2 done clear
  B)
             1 done clear
  C)
             14 done clear
  D)
             8 done clear
  View Solution play_arrow

• question_answer61)
  The value of \[aa'+\,bb'+\,cc'\]being negative the origin will lie in the acute angle between the planes \[an+by+cz+d=0\] and \[a'x+b'y+c'z+d'=0\], if [MP PET 2003]
  A)
             \[a=a'=0\]                                  done clear
  B)
             d and \[d'\]are of same sign done clear
  C)
             d and \[d'\]are of opposite sign done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer62)
  The equation of the plane passing through (1, 1, 1) and        (1, ?1, ?1) and perpendicular to \[2x-y+z+5=0\]is [EAMCET 2003]
  A)
             \[2x+5y+z-8=0\] done clear
  B)
             \[x+y-z-1=0\] done clear
  C)
             \[2x+5y+z+4=0\] done clear
  D)
             \[x-y+z-1=0\] done clear
  View Solution play_arrow

• question_answer63)
  A plane \[\pi \] makes intercepts 3 and 4 respectively on z-axis and x-axis. If \[\pi \] is parallel to y-axis, then its equation is                                                               [EAMCET 2003]
  A)
             \[3x+4z=12\] done clear
  B)
             \[3z+4x=12\] done clear
  C)
             \[3y+4z=12\] done clear
  D)
             \[3z+4y=12\] done clear
  View Solution play_arrow

• question_answer64)
  \[XOZ\]plane divides the join of (2, 3, 1) and (6, 7, 1) in the ratio [EAMCET 2003]
  A)
             3 : 7 done clear
  B)
             2 : 7 done clear
  C)
             ? 3 : 7 done clear
  D)
             ? 2 :7 done clear
  View Solution play_arrow

• question_answer65)
  The equation of the plane through the intersection of the planes \[x+y+z=1\] and \[2x+3y-z+4=0\] parallel to \[x-\]axis is [Orissa JEE 2003]
  A)
             \[y-3z+6=0\] done clear
  B)
             \[3y-z+6=0\] done clear
  C)
             \[y+3z+6=0\] done clear
  D)
             \[3y-2z+6=0\] done clear
  View Solution play_arrow

• question_answer66)
  Distance between two parallel planes \[2x+y+2z=8\] and \[4x+2y+4z+5=0\] is [AIEEE 2004]
  A)
             \[\frac{9}{2}\] done clear
  B)
             \[\frac{5}{2}\] done clear
  C)
             \[\frac{7}{2}\] done clear
  D)
             \[\frac{3}{2}\] done clear
  View Solution play_arrow

• question_answer67)
  The angle between two planes \[x+2y+2z=3\] and \[-5x+3y+4z=9\] is [MP PET 2004]
  A)
             \[{{\cos }^{-1}}\frac{3\sqrt{2}}{10}\] done clear
  B)
             \[{{\cos }^{-1}}\frac{19\sqrt{2}}{30}\] done clear
  C)
             \[{{\cos }^{-1}}\frac{9\sqrt{2}}{20}\] done clear
  D)
             \[{{\cos }^{-1}}\frac{3\sqrt{2}}{5}\] done clear
  View Solution play_arrow

• question_answer68)
  If the points \[(1,\,1,\,k)\] and \[(-3,\,0,\,1)\] be equidistant from the plane \[3x+4y-12z+13=0\],then k =
  A)
             0 done clear
  B)
             1 done clear
  C)
             2 done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer69)
  If O be the origin and the co-ordinates of P be (1, 2, ?3), then the equation of the plane passing through P and perpendicular to OP is       
  A)
             \[x-2y+3z+12=0\] done clear
  B)
             \[2x+3y-z-11=0\] done clear
  C)
             \[x+2y-3z-14=0\] done clear
  D)
             \[x+2y-3z=0\] done clear
  View Solution play_arrow

• question_answer70)
  The equation of the plane passing through the points (0, 1, 2) and (?1, 0, 3) and perpendicular to the plane            \[2x+3y+z=5\] is [J & K 2005]
  A)
             \[3x-4y+18z+32=0\] done clear
  B)
             \[3x+4y-18z+32=0\] done clear
  C)
             \[4x+3y-17z+31=0\] done clear
  D)
             \[4x-3y+z+1=0\] done clear
  View Solution play_arrow

• question_answer71)
  A line joining the points (1, 2, 0) and (4, 13, 5) is perpendicular to a plane. Then the coefficients of x, y and z in the equation of the plane are respectively [J & K 2005]
  A)
             5, 15, 5 done clear
  B)
             3, 11, 5 done clear
  C)
             3, ?11, 5 done clear
  D)
             ? 5, ? 15, 5 done clear
  View Solution play_arrow

• question_answer72)
  If the distance of the point (1, 1,1) from the origin is half its distance from the plane \[x+y+z+k=0\], then \[k=\]                              [Kerala (Engg.)2005]
  A)
             \[\pm 3\] done clear
  B)
             \[\pm 6\] done clear
  C)
             ?3, 9 done clear
  D)
             \[3,\,-9\]                                    done clear
  View Solution play_arrow

• question_answer73)
  If a plane meets the co-ordinate axes at A,B and C such that the centroid of the triangle is (1, 2, 4) then the equation of the plane is [Kerala (Engg.) 2005]
  A)
             \[x+2y+4z=12\] done clear
  B)
             \[4x+2y+z=12\] done clear
  C)
             \[x+2y+4z=3\] done clear
  D)
             \[4x+2y+z=3\] done clear
  E)
             \[x+y+z=12\] done clear
  View Solution play_arrow

• question_answer74)
  If for a plane, the intercepts on the coordinate axes are 8, 4, 4 then the length of the perpendicular from the origin on to the plane is [Kerala (Engg.) 2005]
  A)
             8/3 done clear
  B)
             3/8 done clear
  C)
             3 done clear
  D)
             4/3 done clear
  E)
             4/5 done clear
  View Solution play_arrow