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