find equation of a plane P containing 2 points and parallel to a cross vector

Question

Given: A(0,3,1), B(1,1,4), A'(0,1,0), B'(1,-3,3). Find the equation of plane (P) containing A and B and parallel to the vector AB x A'B'. Find the equation of plane (Q) containing A' and B' and parallel to the vector AB x A'B'.

Answer 1

Hint 1: You have a vector tangent to a plane, and two points on the plane. Can you construct a normal vector to the plane?

Hint 2: If $p$ is a point on a plane, and $n$ is the plane's normal vector, what does the scalar $$n\cdot(x-p)$$ measure, for points $x$?