Exercise · ZW-CURL-005 · ★★☆ Intermediate
Evaluate \(\operatorname{curl}\mathbf F\) at \((1,1,1)\) for \(\mathbf F=\langle x^2y,\,y^2z,\,z^2x\rangle\).
Choose one option.
Show answer
- D. \(\langle -1,\,-1,\,-1\rangle\)
Explanation
\(\operatorname{curl}\mathbf F=\langle -y^2,\,-z^2,\,-x^2\rangle\), since \(R_y-Q_z=0-y^2\), \(P_z-R_x=0-z^2\), \(Q_x-P_y=0-x^2\). At \((1,1,1)\) it is \(\langle -1,-1,-1\rangle\).
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.
\[\operatorname{curl}\mathbf F=\nabla\times\mathbf F=\langle R_y-Q_z,\;P_z-R_x,\;Q_x-P_y\rangle\]
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