Skip to main content\(\newcommand{\R}{\mathbb{R}}
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An interactive three dimensional plot is shown with a curve that sweeps through a box in space. TThe 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 purple arrow is labeled
\(\va\text{.}\) The green arrow is labeled
\(\vN\text{.}\)