Question

If $(2,3,-1)$ is the foot of the perpandicular from $(4,2,1)$ to a plane, the equation of the plane is

• A. $2x-y-2z-3=0$
• B. $-2x+y-2z=1$
• C. $2x+y+2z-5=0$
• D. $2x-y+2z+1=0$

Answer 1

The correct option is B $-2x+y-2z=1$

Given that,

$\overrightarrow{AB}=\left(-2,1,-2\right)$

$\overrightarrow{AB}$ is parallel to normal vector of plane.

$\pi =-2\left(x-2\right)+y-3-2\left(z+1\right)=0$

Equation of plane :$-2x+y-2z=1$

Then,

We get $-2x+y-2z=1$

Option $B$ is correct answer.