Definition:Scalar Projection/Definition 2
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Definition
Let $\mathbf u$ and $\mathbf v$ be vector quantities.
The scalar projection of $\mathbf u$ onto $\mathbf v$ is defined and denoted:
- $u_{\parallel \mathbf v} = \dfrac {\mathbf u \cdot \mathbf v} {\norm {\mathbf v} }$
where:
- $\cdot$ denotes the dot product
- $\norm {\mathbf v}$ denotes the magnitude of $\mathbf v$.
Also known as
The scalar projection of $\mathbf u$ onto $\mathbf v$ is also known as:
- the scalar component
- the scalar resolution
- the scalar resolute
of $\mathbf u$ in the direction of $\mathbf v$.
The notation for $u_{\parallel \mathbf v}$ also varies throughout the literature.
The following forms can sometimes be seen:
- $u_1$
- $\norm {\proj_\mathbf v \mathbf u}$
Also see
Sources
- Weisstein, Eric W. "Projection." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Projection.html