GATE 2024 MT – Question 31
The divergence of $\mathbf V=x^2y\hat i+y^3z\hat j+z^4\hat k$ at $(1,1,1)$ is ______ (nearest integer).
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Correct answer: 9 to 9
Explanation
$\nabla\cdot\mathbf V=\partial_x(x^2y)+\partial_y(y^3z)+\partial_z(z^4)=2xy+3y^2z+4z^3$.
At $(1,1,1)$, this is $2+3+4=\boxed9$.