GATE CE 2019 Set 2 — Question 14
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Engineering Mathematics → Vector Calculus → Gradient, Divergence & Curl
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Question
What is curl of the vector field
2x2yi+5z2j−4yzk?
Correct answer
(D) -14zi - 2x²k
Solution
The curl of a vector field
F=Fxi+Fyj+Fzk is given by:
∇×F=i∂x∂Fxj∂y∂Fyk∂z∂FzGiven
F=2x2yi+5z2j−4yzk:
- i component: ∂y∂(−4yz)−∂z∂(5z2)=−4z−10z=−14z
- j component: −(∂x∂(−4yz)−∂z∂(2x2y))=−(0−0)=0
- k component: ∂x∂(5z2)−∂y∂(2x2y)=0−2x2=−2x2
Thus,
curl F=−14zi−2x2k.
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