Definition:Vector Projection/Definition 2

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 $\mathbf v$.


 * Vector-projection.png

Also see

 * Equivalence of Definitions of Vector Projection