The divergence of the vector field $\vec{F} = (x^2y)\hat{i} - (z^3-3x)\hat{j} + (4y^2)\hat{k}$ at $x = 1$, $y = 2$ and $z = 3$ is ______
Official Answer Key:
4 to 4
Step-by-Step Solution & Explanation
• div F = ∂/∂x(x²y) + ∂/∂y[–(z³–3x)] + ∂/∂z(4y²).
• ∂/∂x(x²y) = 2xy.
• ∂/∂y[–(z³–3x)] = 0 (no y dependence).
• ∂/∂z(4y²) = 0 (no z dependence).
• div F = 2xy. At x=1, y=2: div F = 2(1)(2) = 4.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.