Let $P_1$ be the plane through the origin containing the vectors $[1,2,-1]$ and $[0,1,1]$. Let $P_2$ be the plane through the point $(1,1,1)$ parallel to the vectors $[-1,2,2]$ and $[3,4,-2]$
I know how to find the standard form of a plane that passes through a point and contains a line, but not one that contains two lines.
Find an equation for $P_1$ in normal form $ax+by+cz=0$
The planes $P_1$ and $P_2$ intersect in a line. Find a parametric equation for this line.