JEE Main & Advanced
Sample Paper
JEE Main - Mock Test - 18
question_answer
If \[(2,3,-1)\] is the foot of the perpendicular from \[(4,2,1)\] to a plane, then the equation of the plane
A)\[2x-y-2z-3=0\]
B)\[2x+y-2z-9=0\]
C)\[2x+y+2z-5=0\]
D)\[2x-y+2z+1=0\]
Correct Answer:
D
Solution :
Where \[M\,({{x}_{1}},{{y}_{1}},{{z}_{1}})=(2,3,-1)\] Let, \[M(2,3,-1)\] is the foot of the perpendicular from the point P. The line PM is the normal to the plane. \[\therefore \] DR's of the normal are \[(4-2),\,(2-3),(1+1)\] \[=2,\,-1,\,2=a,b,c\] \[\therefore \] required palne, \[a(x-{{x}_{1}})+b(y-{{y}_{1}})+c(z-{{z}_{1}})=0\] \[2(x-2)+(-1)(y-3)+2(z+1)=0\] \[2x-y+2z+1=0\]