Exercise · ZW-VECTOR-FIELD-IN-PLANE-AND-SPACE-006 · ★★☆ Intermediate
At which point does the field \(\mathbf F(x,y,z)=\langle x-1,\,y+2,\,z\rangle\) vanish?
Choose one option.
Show answer
- A. \((1,-2,0)\)
Explanation
Solve \(x-1=0\), \(y+2=0\), \(z=0\) to get \((1,-2,0)\).
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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