Exercise · ZW-CONSERVATIVE-FIELD-010 · ★★★ Advanced
Let \(\mathbf F=\langle yz,\,xz,\,xy\rangle\). Compute \(\int_C\mathbf F\cdot d\mathbf r\) for any curve from \((1,1,1)\) to \((2,3,2)\).
Choose one option.
Show answer
- A. \(11\)
Explanation
\(\mathbf F=\nabla(xyz)\), so the integral is \(f(2,3,2)-f(1,1,1)=12-1=11\). Answering \(12\) forgets to subtract the value at the start.
Review the concept: Conservative field
A vector field \(\mathbf F\) is conservative if it is the gradient of a scalar function \(f\), called a potential function of \(\mathbf F\).
\[\mathbf F=\nabla f\]
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