Determine the vector and parametric equations of the plane containing the points A (-3,2,8) B (4,3,9) and C (-2,-1,3) (Note: Use point A as your position vector and create direction vectors AB and AC)

Answer 1

Vector AB =(4 + 3, 3 - 2, 9 - 8) = (7, 1, 1); Vector AC = (- 2 + 3, - 1 - 2, 3 - 8) = (1, - 3, - 5). So vector equation of plane r = (- 3, 2, 8) + s(7, 1, 1) + t(1, - 3, - 5), where s and t any real numbers. Now parametric equations:

x = - 3 + 7s + t; y = 2 + s - 3t, z = 8 + s - 5t