Exercise · ZW-VECTOR-FIELD-IN-PLANE-AND-SPACE-003 · ★☆☆ Basic
For \(\mathbf F(x,y)=\langle x,\,y\rangle\), which vector is assigned to the point \((3,-2)\)?
Choose one option.
Show answer
- D. \(\langle 3,-2\rangle\)
Explanation
The field assigns to each point its own position vector: \(\mathbf F(3,-2)=\langle 3,-2\rangle\).
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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