# GATE Questions & Answers of Vector Identities

## What is the Weightage of Vector Identities in GATE Exam?

Total 4 Questions have been asked from Vector Identities topic of Calculus subject in previous GATE papers. Average marks 1.50.

Let $\nabla .\left(f\mathbf{v}\right)={x}^{2}y+{y}^{2}z+{z}^{2}x$,where f and v are scalar and vector fields respectively. If $\mathbf{v}\mathbf{=}y\mathbit{i}+z\mathbit{j}+x\mathbit{k}$ then $\mathbf{v}\mathbf{.}\nabla f$is

The curl of the gradient of the scalar field defined by $V=2{x}^{2}y+3{y}^{2}z+4{z}^{2}x$ is

The direction of vector A is radially outward from the origin, with $\left|A\right|=k{r}^{n}$ where r2 = x2 +y2 +z2 and k is a constant. The value of n for which $\nabla ·A=0$ is

The two vectors [1,1,1] and [1,a,a2] where $a=\left(-\frac{1}{2}+\mathrm{j}\frac{\sqrt{3}}{2}\right)$ are