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\textbf{Vector Functions and Curves}

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

If the position and velocity of a particle satisfy
$\underline{r}\bullet\underline{v}>0$, what does this tell you about the motion of
the particle. What if $\underline{r}\bullet\underline{v}<0$?


\textbf{Answer}

If $\underline{r} \bullet \underline{v} >0$ then $|\underline{r}|$ is
increasing.

So $\underline{r}$ is moving away from the origin. The converse is
also true.

If $\underline{r} \bullet \underline{v} <0$ then $|\underline{r}|$ is
decreasing and it can be seen that $\underline{r}$ is moving
towards the origin.

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