Exercise · ZW-VECTOR-FIELD-IN-PLANE-AND-SPACE-007 · ★★☆ Intermediate
Let \(\mathbf F=\langle x,0,z\rangle\) and \(\mathbf G=\langle y,y,-z\rangle\). Compute \((\mathbf F+\mathbf G)(1,2,3)\).
Choose one option.
Show answer
- D. \(\langle 3,2,0\rangle\)
Explanation
\(\mathbf F+\mathbf G=\langle x+y,\,y,\,0\rangle\), which at \((1,2,3)\) gives \(\langle 3,2,0\rangle\). The third component \(z-z\) cancels.
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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