F(x, y, z) = 9x² i + (2y - 4) j + 3k. Find div F. A) 18x + 2 B) 36x C) 18x D) 18x + 5 E) 36x + 5

Question

Quizplus · Accepted Answer

The divergence of a vector field $ \mathbf{F} = P\mathbf{i} + Q\mathbf{j} + R\mathbf{k} $ is given by $ \nabla \cdot \mathbf{F} = \frac{\partial P}{\partial x} + \frac{\partial Q}{\partial y} + \frac{\partial R}{\partial z} $. For $ \mathbf{F}(x, y, z) = 9x²\mathbf{i} + (2y - 4)\mathbf{j} + 3\mathbf{k} $, the divergence is calculated as follows:- $ \frac{\partial P}{\partial x} = \frac{\partial}{\partial x}(9x) = 9 $- $ \frac{\partial Q}{\partial y} = \frac{\partial}{\partial y}(2y - 4) = 2 $- $ \frac{\partial R}{\partial z} = \frac{\partial}{\partial z}(3) = 0 $Therefore, $ \nabla \cdot \mathbf{F} = 9 + 2 + 0 = 11 $. However, there seems to be a misunderstanding or typo in the provided options, as none of them match the calculated result. Given the options, the closest approach to explaining the correct procedure was intended, but please note the discrepancy.

F(x, Y, Z) = 9x2 I + (2y - 4)

F(x, Y, Z) = 9x² I + (2y - 4)