Find the curl of 2x2y i+5z2 j-4yz k.

$6z\hat i-8xy\hat j+2x^2y\hat k$

$-14z\hat i+6y\hat j+2x^2\hat k$

GATE 2019 CE (CE2) – Question 14

Engineering Mathematics · Calculus: Integrals, partial and total derivatives, gradient, divergence, curl, line, surface and volume integrals · 1 mark · Multiple choice

Find the curl of $2x^2y\hat i+5z^2\hat j-4yz\hat k$.

$6z\hat i+4x\hat j-2x^2\hat k$
$6z\hat i-8xy\hat j+2x^2y\hat k$
$-14z\hat i+6y\hat j+2x^2\hat k$
$-14z\hat i-2x^2\hat k$

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Correct answer: (D) $-14z\hat i-2x^2\hat k$

Explanation

The curl’s i component is $\partial(-4yz)/\partial y-\partial(5z^2)/\partial z=-14z$. Its j component is zero; its k component is $\partial(5z^2)/\partial x-\partial(2x^2y)/\partial y=-2x^2$. Thus $\nabla\times\vec F=-14z\hat i-2x^2\hat k$: **D**.