[Math] Finding equation for line passing through point A and parallel to two planes

Question

I have a homework question asking to find the equation for a line that passes through the point A(-1,0,2) and that is parallel to the planes 2x-y+z=5 and x+2y-z-4=0
does anybody know how to figure this out?

Answer 1

HINT

Notice that the normal vectors are given by $\textbf{n}_{1} = (2,-1,1)$ and $\textbf{n}_{2} = (1,2,-1)$. Therefore the line's direction is given by the cross product $\textbf{n}_{1}\times\textbf{n}_{2}$.