Example 2

In Kinematics, if $f(t)$ is the position of a moving point $M$ at time $t$, if $g(t)$ is the position at the same instant of the projection $M'$ of $M$ onto a plane $P$ (resp. a line $D$) with kernel a line (resp. a plane) not parallel to $P$ (resp. $D$), then $g$ is the composition of the projection $u$ of $\mathbf{R}^3$ onto $P$ (resp. $D$) and of $f$; since $u$ is a (continuous) linear mapping one sees that the projection of the velocity of a moving point onto a plane (resp. a line) is equal to the velocity of the projection of the moving point onto the plane (resp. line).*