Definition:Scalar Projection/Definition 1

Definition
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 $\mathbf v$.


 * Scalar-projection.png

Also see

 * Equivalence of Definitions of Scalar Projection