Skip to main content\(\newcommand{\R}{\mathbb{R}}
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An interactive two dimensional plot is shown with a curve that moves from the top right to the bottom left. The curve starts moving up before turning to go down and left, then turning up and left. The slider at the top of the figure changes the location of a highlighted point on the curve. There are five arrows drawn starting from the highlighted point. A yellow arrow is drawn from the highlighted point in direction tangent to the curve and a red arrow is drawn in the same direction but longer than the yellow arrow for some points. The red arrow is in the opposite direction for other highlighted points. A green arrow is drawn the same length as the yellow arrow but in a perpendicular direction to the yellow arrow. A blue arrow is shown in the same direction but longer than the green arrow. A purple arrow of changing length depending on the highlighted point is shown that is the sum of the red and blue arrows. A second blue arrow is drawn from the end of the red arrow to the end of the purple arrow. The yellow arrow is labeled
\(\vT\text{.}\) The red arrow is labeled
\(a_{\vT} \vT\text{.}\) The purple arrow is labeled
\(\va\text{.}\) The green arrow is labeled
\(\vN\text{.}\) The blue arrow is labeled
\(a_{\vN} \vN\text{.}\)