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Contents Index Calc Dark Mode Prev Up Next \(\newcommand{\R}{\mathbb{R}}
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Activity 13.4.6 .
Explain why neither of the vector fields in
Figure 13.4.4 is path-independent.
A vector field in which all vectors are horizontal. The vectors are \(0\) along the \(x\) -axis, point to the right for \(y>0\) and point to the left for \(y\lt 0\text{.}\) Vectors get longer as distance from the \(x\) -axis increases.
(a) \(\vF\) A vector field in which vectors appear to circulate in a clockwise manner around the point \((3,0)\text{.}\) The magnitude of vectors increases with the distance from \((3,0)\text{.}\) The plot shows the portion of the vector field with \(0\leq x\leq 6\) and \(-3\leq y\leq 3\text{.}\)
(b) \(\vG\) Figure 13.4.4. Two vector fields that are not path-independent.
