Image: Dot product as projection onto a unit vector
The dot product of vectors $\vc{a}$ and unit vector $\vc{u}$ is the projection of $\vc{a}$ onto $\vc{u}$, i.e., $$\vc{a}\cdot \vc{u} = \|\vc{a}\| \cos\theta,$$
where $\theta$ is the angle between $\vc{a}$ and $\vc{u}$. This expression does not involve the magnitude of $\vc{u}$ since it is normalized to be length one.
Image file: dot_product_projection_unit_vector.png
Source image file: dot_product_projection_unit_vector.svg
Source image type: Inkscape SVG
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