Exercise · ZW-CURL-003 · ★☆☆ Basic
Compute \(\operatorname{curl}\mathbf F\) for \(\mathbf F=\langle xy,\,yz,\,zx\rangle\).
Choose one option.
Show answer
- B. \(\langle -y,\,-z,\,-x\rangle\)
Explanation
\(R_y-Q_z=0-y\), \(P_z-R_x=0-z\), \(Q_x-P_y=0-x\). All three terms are negative: \(\langle -y,-z,-x\rangle\).
Review the concept: Curl
The curl of a vector field \(\mathbf F=\langle P,Q,R\rangle\) is the vector field that measures, at each point, the field's tendency to rotate, with axis and rate of rotation given by its direction and length.
\[\operatorname{curl}\mathbf F=\nabla\times\mathbf F=\langle R_y-Q_z,\;P_z-R_x,\;Q_x-P_y\rangle\]
More practice problems: curl
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