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Multiplying $\vec r(t)$ by 5 scales the function by 5, producing $5\vec r(t) = \langle 5\cos t+1,5\sin t+1.5\rangle$, which is graphed in Figure \ref{fig:vvf3}(c) along with $\vec r(t)$. The new function is ``5 times bigger'' than $\vec r(t)$. Note how the graph of $5\vec r(t)$ in (c) looks identical to the graph of $\vec r(t)$ in $(b)$. This is due to the fact that the $x$ and $y$ bounds of the plot in $(c)$ are exactly 5 times larger than the bounds in (b). |
$5\vec r(t) = \langle 5\cos t+1,5\sin t+1.5\rangle$
should be
$5\vec r(t) = \langle 5\cos t+t,5\sin t+\frac32 t\rangle$
