Dot Product (Projection) - Maple Help

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Dot Product (Projection)

Main Concept

Given two vectors  $\stackrel{\mathbf{⇀}}{\mathbit{a}}$ and $\stackrel{\mathbf{⇀}}{\mathbit{b}}$, their dot product is the scalar quantity

 where θ is the angle between $\stackrel{⇀}{a}$ and $\stackrel{⇀}{b}$.

The dot product can also be expressed in terms of the components of $\stackrel{⇀}{a}$ and $\stackrel{⇀}{b}$ as follows:



The unit vector in the direction of  $\stackrel{⇀}{a}$ is given by

$\stackrel{^}{a}=\frac{\stackrel{⇀}{a}}{\left|a\right|}$

The vector projection of  $\stackrel{⇀}{a}$ on $\stackrel{⇀}{b}$ is the orthogonal projection of $\stackrel{⇀}{a}$ onto the line in the direction of $\stackrel{⇀}{b}$:

The scalar projection of  $\stackrel{⇀}{a}$ on $\stackrel{⇀}{b}$ is the length of the associated vector projection.

Click and or drag on the graph to change the two vectors. See how they affect the scalar and vector projections.

   





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