#geometry 

## Scalar projection
![[Pasted image 20240917195427.png]]
$$\LARGE s=\frac{\vec{a} \cdot \vec{b}}{|b|}$$, where $\LARGE \vec{a}\cdot \vec{b}$ is the [[Скалярное произведение векторов|dot product]]

## Vector projection
$$\LARGE proj_b\vec{a}=a_1 \hat{b}$$
where $\LARGE a_1$ is the scalar projection, and $\LARGE \hat{b}$ is the [[Орт|unit vector]] in the direction of $\LARGE \vec{b}$.

$$\LARGE proj_b\vec{a}=\frac{\vec{a}\cdot\vec{b}}{|b|}\cdot\frac{\vec{b}}{|b|}$$