Question

The projection of the line $L:\frac{x+1}{-1}=\frac{y}{2}=\frac{z-1}{3}$ on the plane $\pi :x-2y+z=6$ is the line of intersection of this plane $\pi$ with the plane (containing the line $L$)

• A. $2x+y+2=0$
• B. $3x+y-z=2$
• C. $2x-3y+8z=3$
• D. none of these

Answer 1

The correct option is A $2x+y+2=0$

Equation of the plane through $(-1,0,1)$ is $a(x+1)+b(y-0)+c(z-1)=0\dots \left(1\right)$
which is parallel to the given line and perpendicular to the given plane.
$-a+2b+3c=0\dots \left(2\right)$ and
$a-2b+c=0\dots \left(3\right)$
From Eqs. $\left(2\right)$ and $\left(3\right),$ we get
$c=0,a=2b$

From Eq. $\left(1\right)$, $2b(x+1)+by=0$
$\Rightarrow 2x+y+2=0$