Question

Find an equation of the plane. The plane through the points (0, 7, 7), (7, 0, 7), and (7, 7, 0).

Answer 1

x + y + z = 14

Explanation:

If the points are designated A, B, C, then ...

AB × AC = (7, -7, 0) × (7, 0, -7) = (49, 49, 49).

That is, a vector perpendicular to the plane is (1, 1, 1), so the equation of the plane can be ...

(1, 1, 1)·(x, y, z) = (1, 1, 1)·A

x + y + z = 14