Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

The locus of Q is the line of intersection of the plane $x+2y+3z=4$ and the plane through P perpendicular to (1,1,1), i.e. $1(x-1)+1(y-1)+1(z-1)=0$. Its direction is $(1,1,1)\times (1,2,3)=(1,-2,1)$ and it passes through $(0,5,-2)$. So the line is $\frac{x}{1}=\frac{y-5}{-2}=\frac{z+2}{1}$.