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Contents Index Calc Dark Mode Prev Up Next \(\newcommand{\R}{\mathbb{R}}
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Activity 10.2.3 .
(a)
Let
\begin{equation*}
\vr(t) = \cos(t) \vi - \sin(t) \vj + t \vk.
\end{equation*}
Sketch the curve using some appropriate tool and make a drawing by hand that labels the point at the terminal point of \(\vr(\pi)\text{.}\)
(b) Recall that we discussed earlier that the vector
\(\vr\, '(a)\) is tangent to the graph of
\(\vr(t)\) at the point where
\(t=a\text{.}\) Find a direction vector for the line tangent to the graph of
\(\vr\) at the point where
\(t=\pi\text{.}\)
(c) Find the parametric equations of the line tangent to the graph of
\(\vr\) when
\(t=\pi\text{.}\)
(d) On your plot of the curve
\(\vr(t)\text{,}\) sketch the tangent line corresponding to
\(t = \pi\) and highlight the role of
\(\vr\, '(\pi)\) on your plot.
