Definition:Vector Projection/Definition 3

Definition
Let $\mathbf u$ and $\mathbf v$ be vector quantities.

The (vector) projection of $\mathbf u$ onto $\mathbf v$ is defined and denoted:


 * $\proj_\mathbf v \mathbf u = u_{\parallel \mathbf v} \mathbf {\hat v}$

where:
 * $u_{\parallel \mathbf v}$ denotes the scalar projection of $\mathbf u$ on $\mathbf v$
 * $\mathbf {\hat v}$ denotes the unit vector in the direction of $\mathbf v$.


 * Vector-projection.png

Also see

 * Equivalence of Definitions of Vector Projection