Study guide and 4 practice problems on:

## Component along a vector

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.