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, \[a(x-{{x}_{1}})+b(y-{{y}_{1}})+c(z-{{z}_{1}})=0\] \[2(x-2)+(-1)(y-3)+2(z+1)=0\] \[2x-y+2z+1=0\]