The Projection command obtains the projection from the first input parameter onto the second input parameter, where the first parameter can be a point, a vector, or a line, and the second parameter can be a vector, a line, or a plane.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{MultivariateCalculus}\right]\right)\:$

$\mathrm{Projection}\left(⟨1\,0\,-3⟩\,⟨3\,2\,0⟩\right)$

$\left[\begin{array}{c}\frac{9}{13}\\ \frac{6}{13}\\ 0\end{array}\right]$

$\mathrm{Projection}\left(\left[1\,2\right]\,\mathrm{Line}\left(\left[0\,0\right]\,⟨a\,1⟩\right)\right)$

$\left[\frac{\left(2+a\right)a}{a^2+1}\,\frac{2+a}{a^2+1}\right]$

$\mathrm{Projection}\left(\left[5\,1\,2\right]\,\mathrm{Plane}\left(\left[0\,0\,0\right]\,⟨0\,0\,1⟩\right)\right)$

$\left[5\,1\,0\right]$

$L≔\mathrm{Projection}\left(\mathrm{Line}\left(\left[1\,2\,1\right]\,⟨1\,0\,1⟩\right)\,\mathrm{Plane}\left(\left[1\,0\,3\right]\,⟨1\,1\,2⟩\right)\right)\:$

$\mathrm{GetRepresentation}\left(L\,\mathrm{form}=\mathrm{equations}\right)$

$\left\{z=\frac{5}{3}\,x+y=\frac{11}{3}\right\}$

The Student[MultivariateCalculus][Projection] command was introduced in Maple 18.

For more information on Maple 18 changes, see Updates in Maple 18.