Exercise · ZW-VECTOR-FIELD-IN-PLANE-AND-SPACE-004 · ★☆☆ Basic
Let \(\mathbf F(x,y)=\langle -y,\,x\rangle\). Find \(\|\mathbf F(3,4)\|\).
Choose one option.
Show answer
- B. \(5\)
Explanation
\(\mathbf F(3,4)=\langle -4,3\rangle\) and \(\sqrt{16+9}=5\). A common slip is leaving \(25\) without taking the square root.
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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