Vector projections
This applet aims to demonstrate visually the projection of a vector v onto a vector u. The bold line is the result of that projection.
The notion can be likened to having a light source perpendicular to $\bf{u}$, in which $\text{proj}_{\bf{u}}({\bf{v}})$ can be seen as the shadow of $\bf v$ cast onto $\bf u$.
Other resources: