Exercise · ZW-VECTOR-FIELD-IN-PLANE-AND-SPACE-008 · ★★☆ Intermediate
Let \(\mathbf F(x,y,z)=\langle x,y,z\rangle\). Where is \(\|\mathbf F\|=2\)?
Choose one option.
Show answer
- B. on the sphere \(x^2+y^2+z^2=4\)
Explanation
\(\|\mathbf F\|=\sqrt{x^2+y^2+z^2}=2\) is equivalent to \(x^2+y^2+z^2=4\); the squared radius is \(4\), not \(2\).
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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