5. Determine an equation for the plane that is exactly between the points A(-1, 2, 4) and B(3, 1, -4).

Answer 1

vector AB must be the normal to the plane
vector AB = (4,-1,-8)

so the plane must have equation:
4x - y - 8z = c
but the midpoint of AB must lie on it, and that midpoint is (1, 3/2, 0)
sub it in ...

4 - 3/2 - 0 = c
c = 5/2

plane equation:
4x - y - 8z = 5/2 or in only integers
8x - 2y - 16z = 5