GATE CH 2023 | Question: 12

Question

The vector $\overrightarrow{\boldsymbol{v}}$ is defined as

$$\overrightarrow{\boldsymbol{v}}=z x \hat{\imath}+2 x y \hat{\jmath}+3 y z \hat{k} .$$

Which one of the following is the CORRECT value of divergence of $\vec{v}$, evaluated at the point $(x, y, z)=(3,2,1)$ ?

• A. $0$
• B. $3$
• C. $14$
• D. $13$

Answer 1

V = zxî + 2xyĵ + 3yzƙ

Divergence of V = z + 2x + 3y

Divergence of V at the point (3,2,1) = 1+6+6 = 13