Exercise · ZW-VECTOR-FIELD-IN-PLANE-AND-SPACE-001 · ★☆☆ Basic
Let \(\mathbf F(x,y,z)=\langle xy,\,z,\,x+y\rangle\). Compute \(\mathbf F(1,2,3)\).
Choose one option.
Show answer
- C. \(\langle 2,3,3\rangle\)
Explanation
Substitute \(x=1,y=2,z=3\): \(xy=2\), \(z=3\), \(x+y=3\).
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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