For v=3x2y i+8y2z j+5xyz k, find its curl.

$-3x^2\hat i-8y^2\hat j+5z(x+y)\hat k$

$6xy\hat i-16yz\hat j+5xy\hat k$

GATE 2020 CH – Question 13

Engineering Mathematics · Calculus: Gradient, divergence, curl, vector identities and integral theorems · 1 mark · Multiple choice

For $\mathbf v=3x^2y\hat i+8y^2z\hat j+5xyz\hat k$, find its curl.

$-3x^2\hat i-8y^2\hat j+5z(x+y)\hat k$
$6xy\hat i-16yz\hat j+5xy\hat k$
$(5xz-8y^2)\hat i-5yz\hat j-3x^2\hat k$
$y(11x+16z)$

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Show answer and explanation

Correct answer: (C) $(5xz-8y^2)\hat i-5yz\hat j-3x^2\hat k$

Explanation

The curl components are $\partial v_z/\partial y-\partial v_y/\partial z=5xz-8y^2$, $\partial v_x/\partial z-\partial v_z/\partial x=-5yz$, and $\partial v_y/\partial x-\partial v_x/\partial y=-3x^2$. These give C. The scalar expression in D is the divergence, not the vector curl.

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