Question

Find the divergence of this given vector  $\vec{F}=x^3 y\vec{i}+3xy^2 z\vec{j}+3zx\vec{k}$.

(a) 3x^2 y+6xyz+x

(b) 2x^2 y+6xyz+3x

(c) 3x^2 y+3xyz+3x

(d) 3x^2 y+6xyz+3x

The question was posed to me during a job interview.

The question is from Using Properties of Divergence and Curl in section Vector Differential Calculus of Engineering Mathematics

Answer 1

The correct option is (d) 3x^2 y+6xyz+3x

Best explanation: We know that divergence of a vector is given by

$\bigtriangledown.\vec{F}=\frac{\partial(x^3 y)}{\partial x}+\frac{\partial(3xy^2 z)}{\partial y}+\frac{\partial(3xz)}{\partial z}$

$\bigtriangledown.\vec{F}=3x^2 y+6xyz+3x$.