The plane passes through $(3,2,-1)$ and $(1,-1,2)$ and is parallel to the line $v=(1,-1,0) + t(3,2,-2)$
I know how to do this with a vector perpendicular to the plane and that passes through a point, but I'm clueless on this one
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Hint: Use the two points in the plane to get a second direction that lies in the plane, in addition to the direction from the line. Then write down a third vector that's perpendicular to these two (perhaps by considering the cross product).