Scalar Projection

Scalar Projection is the amount one vector "goes along" another: the length of the shadow that vector $\vec{s}$ casts onto vector $\vec{r}$.

It's calculated using the Dot Product divided by the Vector Magnitude of the vector being projected onto:

$\text{scalar projection of } \vec{s} \text{ onto } \vec{r} = \frac{\vec{r} \cdot \vec{s}}{|\vec{r}|} = |\vec{s}| \cos\theta$

where $\theta$ is the angle between the two vectors. The result is a single number (a Scalar), and it's negative when the angle is more than 90°.

See Week 2 - Vectors are objects that move around space.