F(x, y, z) = 4xy i + 4xyz j + (z² - 4zx)k. Find div F. A) 0 B) 4xy + 4xyz + 4x C) 4y + 4xz + 2z - 4x D) 2z E) 4xy + z²

Question

Quizplus · Accepted Answer

To find the divergence of F, we need to take the dot product of the del operator with F. del(F) = (∂/∂x i + ∂/∂y j + ∂/∂z k ) · (4xy i + 4xyz j + (z² - 4zx)k) = (4y + 0 + 0) i + (4xz + 4xy + 0) j + (0 + z² - 4x) k. Therefore, div F = 4y + 4xz - 4x, which is option C.

F(x, Y, Z) = 4xy I + 4xyz J