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Component along a vector

$\newcommand{\bfA}{\mathbf{A}}$ $\newcommand{\bfB}{\mathbf{B}}$ $\newcommand{\bfC}{\mathbf{C}}$ $\newcommand{\bfF}{\mathbf{F}}$ $\newcommand{\bfI}{\mathbf{I}}$ $\newcommand{\bfa}{\mathbf{a}}$ $\newcommand{\bfb}{\mathbf{b}}$ $\newcommand{\bfc}{\mathbf{c}}$ $\newcommand{\bfd}{\mathbf{d}}$ $\newcommand{\bfe}{\mathbf{e}}$ $\newcommand{\bfi}{\mathbf{i}}$ $\newcommand{\bfj}{\mathbf{j}}$ $\newcommand{\bfk}{\mathbf{k}}$ $\newcommand{\bfn}{\mathbf{n}}$ $\newcommand{\bfr}{\mathbf{r}}$ $\newcommand{\bfu}{\mathbf{u}}$ $\newcommand{\bfv}{\mathbf{v}}$ $\newcommand{\bfw}{\mathbf{w}}$ $\newcommand{\bfx}{\mathbf{x}}$ $\newcommand{\bfy}{\mathbf{y}}$ $\newcommand{\bfz}{\mathbf{z}}$
The component of $\bfx$ along $\bfv$ is the distance along $\bfv$ obtained by dropping down a perpendicular line from $\bfx$.
The component of $\bfx$ along $\bfv$ is $$\text{comp}_\bfv \bfx = \frac{\bfx\cdot \bfv}{\left| \bfv \right|}.$$
If $\theta$ is the angle between $\bfx$ and $\bfv$, the component of $\bfx$ along $\bfv$ is $\left| \bfx \right| \cos \theta$.
A vector component is also called a scalar projection.
A vector component is negative if the two vectors are more than $\pi/2$ apart in angle.

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