F(x, y, z) = (9xy - 9) i + 6xyz j + (z² - 9)k. Find div F. A) 9y + 6xz + 2z B) 9xy + 6xyz + z² C) 0 D) 2z E) 9xy + z²

Question

Quizplus · Accepted Answer

We use the formula for divergence: div F = ∂Fx/∂x + ∂Fy/∂y + ∂Fz/∂z. 
Here, ∂Fx/∂x = 0, ∂Fy/∂y = 6xz, and ∂Fz/∂z = 2z. 
Therefore, div F = 6xz + 2z = 2z(3x + 1). 
None of the answer choices match this expression, but answer choice A is closest as it contains the terms 6xz and 2z.

F(x, Y, Z) = (9xy - 9) I + 6xyz