Question

The value of curl (\(\text{grad } f\)), where \( f = x^2 - 4y^2 + 5z^2 \), is:

• A. 0
• B. 1
• C. \( 4\hat{i} + 2\hat{j} - 3\hat{k} \)
• D. \( 2x\hat{i} - 3y\hat{j} + 2z\hat{k} \)

Hint:

The curl of a gradient is always zero, a fundamental identity in vector calculus.

Answer 1

The Correct Option is A

The curl of the gradient of any scalar field is always zero, i.e., \[ \nabla \times \nabla f = 0. \] Therefore, the value of \(\text{curl} (\text{grad } f)\) is 0.