Category:Definitions/Scalar Projections

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This category contains definitions related to Scalar Projections.
Related results can be found in Category:Scalar Projections.


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


Definition 1

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 $\mathbf v$.


Definition 2

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 $\mathbf v$.


Definition 3

The scalar projection of $\mathbf u$ onto $\mathbf v$ is defined and denoted:

$u_{\parallel \mathbf v} = \mathbf u \cdot \mathbf {\hat v}$

where:

$\cdot$ denotes the dot product
$\mathbf {\hat v}$ denotes the unit vector in the direction of $\mathbf v$.


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Pages in category "Definitions/Scalar Projections"

The following 4 pages are in this category, out of 4 total.