Question

The plane with normal vector <-6, 3, -3> containing the point (7, -4, 5) has equation Ax + By + Cz = D. If A= - 6 find what B, C, and D equals.

Answer 1

Explanation:

for a plane defined as

Ax + By + Cz + D = 0

(A, B, C) is the normal vector (90° with the plane).

so, we know with the given normal vector (-6, 3, -3) that

A = -6

B = 3

C = -3

we are only missing D.

for that we use the given point (7, -4, 5) :

-6×7 + 3×-4 + -3×5 = D

-42 - 12 - 15 = D

-69 = D