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\textbf{Vector Functions and Curves}

\textit{\textbf{One variable functions}}
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\textbf{Question}

Given that the position and velocity vectors of a moving object are
always perpendicular, show that the objects' path lies on a sphere.


\textbf{Answer}

$$\frac{d}{dt}|\underline{r}|^2 = \frac{d}{dt}\underline{r} \bullet
\underline{r} = 2\underline{r} \bullet \underline{v} =0$$
$\Rightarrow$ $|\underline{r}|$ is constant.

Hence $\underline{r}(t)$ lies on a sphere which is centered at the
origin.

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