1. The problem statement, all variables and given/known data Find a Cartesian equation of the plane P containing A (2, 0, −3) , B(1, −1, 6) and C(5, 5, 0) , and determine if point D(3, 2, 3) lies on P. 2. Relevant equations vector cross product ax + by + cz = 0 3. The attempt at a solution Take the cross product of AB and AC to get normal vector. AB = -i -j + 9k AC = 31 + 5j + 3k I used the determinant method at got: AB X AC = -48i + 30j -2k Now as A, B and C lie on P, take a point say A(2, 0, -3) -48(x - 2) +30(y) -2(z + 3) = 0 rearranging that gives: -48x + 30y -2z = -90 Then putting in the x, y and z values for D the equation holds. The question I have is that the answer for the plane given is: 24x − 15y + z = 45 Is there a more common method to follow to get this equation rather than the one I got?