Posted by j on Saturday, May 26, 2012 at 8:11am.
5. Determine an equation for the plane that is exactly between the points A(1, 2, 4) and B(3, 1, 4).

Calculus  Reiny, Saturday, May 26, 2012 at 8:34am
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