Exercise · ZW-VECTOR-FIELD-IN-PLANE-AND-SPACE-009 · ★★★ Advanced
Let \(\mathbf H=\langle1,0,1\rangle\) and \(\mathbf K=\langle1,1,-1\rangle\) be the values of two fields at a point. What is \(2\mathbf H-\mathbf K\) at that point?
Choose one option.
A \(\langle 1,1,3\rangle\) B \(\langle 1,-1,1\rangle\) C \(\langle 1,-1,3\rangle\) D \(\langle 3,1,1\rangle\) Show answer C. \(\langle 1,-1,3\rangle\)← Back to the question
Explanation Work component by component: \(\langle 2-1,\,0-1,\,2-(-1)\rangle=\langle1,-1,3\rangle\). Subtracting \(-1\) adds \(1\).
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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