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Q.
The projection of the line $\frac{x+1}{-1}=\frac{y}{2}=\frac{z-1}{3}$ on the plane $x-2 y+z=6$ is the line of intersection of this plane with the plane
Three Dimensional Geometry
Solution:
Equation of the plane through $(-1,0,1)$ is
$a(x+1)+b(y-0)+c(z-1)=0 \, \dots(i)$
which is parallel to the given line and perpendicular to the given plane
$-a+2 b+3 c=0 \, \dots(ii)$
and $ a-2b+c=0\, \dots(iii)$
From Eqs. (ii) and (iii), we get
$c=0, a=2b$
From Eq. (i), $2 b(x+1)+b y=0$
$\Rightarrow 2 x+y+2=0$