Exercise · ZW-VECTOR-FIELD-IN-PLANE-AND-SPACE-010 · ★★★ Advanced
Let \(\mathbf F(x,y)=\dfrac{\langle -y,\,x\rangle}{x^2+y^2}\). What is \(\|\mathbf F(0,2)\|\)?
Choose one option.
Show answer
- A. \(\tfrac12\)
Explanation
\(\mathbf F(0,2)=\langle -2,0\rangle/4=\langle -\tfrac12,0\rangle\), of length \(\tfrac12\). In general \(\|\mathbf F\|=1/r\), with \(r\) the distance to the origin.
Review the concept: Vector field in the plane and space
A vector field \(\mathbf F\) assigns to each point of a region of the plane or of space a vector; its components \(P,Q,R\) are scalar functions of the coordinates.
\[\mathbf F(x,y,z)=\langle P(x,y,z),\,Q(x,y,z),\,R(x,y,z)\rangle\]
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