Planes

Any three non-collinear points determine a plane (A, B, C are non-collinear if they aren't scalar multiples ).

With three non-collinear points, two distinct direction vectors can be found.

A plane can be defined by two distinct vectors (not scalar multiples) and a point on the plane

A nonzero vector is a is a normal vector if it is orthogonal to the plane (sticking out of the plane)