GATE EC 2017 Set 2 — Question 28
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Engineering Mathematics → Vector Calculus → Gradient, Divergence & Curl
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Question
If the vector function is irrotational, then the values of the constants and , respectively, are
Correct answer
(B) 0.0, 3.0, 2.0
Solution
For a vector function to be irrotational, its curl must be zero, i.e., .
Given .
So, , , .The curl of is given by:
Let's calculate the partial derivatives:
Substitute these into the curl equation:
For the curl to be zero, each component must be zero:
Thus, the values of are .The correct option is (B).
Given .
So, , , .The curl of is given by:
Let's calculate the partial derivatives:
Substitute these into the curl equation:
For the curl to be zero, each component must be zero:
Thus, the values of are .The correct option is (B).
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