\begin{definition}[Definition:Scalar Projection/Definition 1]
Let $\mathbf u$ and $\mathbf v$ be vector quantities.
The '''scalar projection of $\mathbf u$ onto $\mathbf v$''', denoted $u_{\parallel \mathbf v}$, is the magnitude of the orthogonal projection of $\mathbf u$ onto a straight line which is parallel to $\mathbf v$.
Hence $u_{\parallel \mathbf v}$ is the magnitude $\norm {\mathbf u} \cos \theta$, where:
:$\norm {\mathbf u}$ is the magnitude of $\mathbf u$
:$\cos \theta$ is the angle between $\mathbf u$ and $\mathbf v$.
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\end{definition}