Find the equation of a straight line which passes through the point P(3,1,-2) and is perpendicular to the planes L1 and L2, where
L1 : x - 3y + 2z = 2,
L2 : 2x + y - 2z = 5.
find a line in each plane
the cross product of those two vectors is perpendicular to them both.
Then translate the vector so it passes through P.