Question
$\mathbf{F}(x, y)=\frac{x \mathbf{i}+y \mathbf{j}}{\sqrt{x^{2}+y^{2}}} .$ [Note: Each vector in the field is a unit vector in the same direction as the position vector $\mathbf{r}=x \mathbf{i}+y \mathbf{j} .$ ]
Step 1
We can see that each vector in the field is a unit vector in the same direction as the position vector $\mathbf{r}=x \mathbf{i}+y \mathbf{j}$. Show more…
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$\mathbf{F}(x, y)=y \mathbf{i}-x \mathbf{j}$. [Note: Each vector in the field is perpendicular to the position vector $\mathbf{r}=x \mathbf{i}+y \mathbf{j} .]$
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Sketch the following vector fields. $$\mathbf{F}=\left\langle\frac{x}{\sqrt{x^{2}+y^{2}}}, \frac{y}{\sqrt{x^{2}+y^{2}}}\right\rangle$$
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