Consider the points
A : (x, y, z) = (1, 0, 1)
B : (x, y, z) = (0, 5, 3)
C : (x, y, z) = (3, 2, 3)
D : (x, y, z) = (3, -1, 2)
(a) Calculate AB and AC.
(b) Find a vector that is perpendicular to both AB and AC.
(c) What is the area of the triangle with vertices at A, B, and C?
(d) Find a vector equation of the plane that contains the points A, B, and C, and then find a corresponding Cartesian equation ax + by + cz = d of this plane.
(e) Find the minimum distance from this plane to the point D.