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question_answer1) The equation of the plane containing the straight line \[\frac{x}{2}=\frac{y}{3}=\frac{z}{4}\] and perpendicular to the plane containing the straight lines \[\frac{x}{3}=\frac{y}{4}=\frac{z}{2}\] and \[\frac{x}{4}=\frac{y}{2}=\frac{z}{3}\] is \[px+qy+r=0,\] then \[p+q+r\] is
question_answer2) If a line makes angles \[\alpha ,\beta ,\gamma ,\delta \] with four diagonals of a cube, then the value of \[{{\sin }^{2}}\alpha +{{\sin }^{2}}\beta +{{\sin }^{2}}\gamma +{{\sin }^{2}}\delta \] is
question_answer3) The number of straight lines that are equally inclined to the three dimensional co-ordinate axes, is
question_answer4) If the point \[(2,\alpha ,\beta )\] lies on the plane which passes through the points \[(3,4,2)\] and \[(7,0,6)\] and is perpendicular to the plane \[2x-5y=15,\] then \[2\alpha -3\beta \] is equal to
question_answer5) If the lines \[\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}\] and \[\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}\] intersect, then the value of k is
question_answer6) The perpendicular distance from the origin to the plane containing the two lines, and is \[\frac{p}{\sqrt{q}},\] then \[pq\]is
question_answer7) If the straight lines \[x=1+s,\] \[y=-3-\lambda s,\] \[z=1+\lambda s\] and \[x=\frac{t}{2},\] \[y=1+t,\] \[z=2-t,\] with parameters s and t respectively, are co-planar, then \[|\lambda |\] equals.
question_answer8) If the line, \[\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-2}{4}\] meets the plane, \[x+2y+3z=15\] at a point P, then the distance of P from the origin is
question_answer9) The length of the perpendicular from the origin to the plane \[3x+4y+12z=52\] is
question_answer10) Let P be the plane, which contains the line of intersection of the planes, \[x+y+z-6=0\] and \[2x+3y+z+5=0\] and it is perpendicular to the xy-plane. Then the distance of the point \[(0,0,256)\] from P is equal to \[\frac{m}{\sqrt{n}},\] then the value of \[m.n\] is
question_answer11) The distance of the point having position vector \[-\hat{i}+2\hat{j}+6\hat{k}\] from the straight line passing through the point \[(2,3,-4)\] and parallel to the vector, \[6\hat{i}+3\hat{j}-4\hat{k}\] is
question_answer12) If the plane \[x+ay+z=5\] has equal intercepts on axes, then the value of a is
question_answer13) Distance between two parallel planes \[2x+y+2z=8\] and \[4x+2y+4z+5=0\] is
question_answer14) The radius of the circle in which the sphere \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+2x-2y-4z-19=0\] is cut by the plane \[x+2y+2z+7=0\] is
question_answer15) The plane \[x+2y-z=4\] cuts the sphere \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-x+z-2=0\] in a circle whose radius is
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