GATE2019 IN: 2

Question

The vector function $\overrightarrow{A}$ is given by $\overrightarrow{A}$ = $\overrightarrow{\bigtriangledown}$u , where u(x, y) is a scalar function. Then |$\overrightarrow{\bigtriangledown}$  x $\overrightarrow{A}$| is

• A. -1
• B. 0
• C. 1
• D. $\infty$

Answer 1

Given:
A = ∇u (where ∇ represents the gradient operator, del)

We need to find the magnitude of the curl of A: |∇ x A|

Substitute A = ∇u into the expression: |∇ x (∇u)|

A fundamental identity in vector calculus states that the curl of the gradient of any twice-differentiable scalar function is always the zero vector. ∇ x (∇u) = 0

Therefore, the magnitude of the zero vector is simply 0: |0| = 0