Student[MultivariateCalculus] - Maple Programming Help

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Student[MultivariateCalculus]

 Projection
 obtain the projection from one object onto another object

 Calling Sequence Projection(pf, po)

Parameters

 pf - list, Vector, Line ; points or vectors or Line objects defined by Student[MultivariateCalculus]. po - Vector, Line, Plane ; vectors or Line or Plane objects defined by Student[MultivariateCalculus].

Description

 • The Projection command obtains the projection from the first input parameter onto the 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.

Examples

 > $\mathrm{with}\left(\mathrm{Student}[\mathrm{MultivariateCalculus}]\right):$
 > $\mathrm{Projection}\left(⟨1,0,-3⟩,⟨3,2,0⟩\right)$
 $\left[\begin{array}{c}\frac{{9}}{{13}}\\ \frac{{6}}{{13}}\\ {0}\end{array}\right]$ (1)
 > $\mathrm{Projection}\left(\left[1,2\right],\mathrm{Line}\left(\left[0,0\right],⟨a,1⟩\right)\right)$
 $\left[\frac{\left({2}{+}{a}\right){}{a}}{{{a}}^{{2}}{+}{1}}{,}\frac{{2}{+}{a}}{{{a}}^{{2}}{+}{1}}\right]$ (2)
 > $\mathrm{Projection}\left(\left[5,1,2\right],\mathrm{Plane}\left(\left[0,0,0\right],⟨0,0,1⟩\right)\right)$
 $\left[{5}{,}{1}{,}{0}\right]$ (3)
 > $L≔\mathrm{Projection}\left(\mathrm{Line}\left(\left[1,2,1\right],⟨1,0,1⟩\right),\mathrm{Plane}\left(\left[1,0,3\right],⟨1,1,2⟩\right)\right):$
 > $\mathrm{GetRepresentation}\left(L,\mathrm{form}=\mathrm{equations}\right)$
 $\left\{{z}{=}\frac{{5}}{{3}}{,}{x}{+}{y}{=}\frac{{11}}{{3}}\right\}$ (4)

Compatibility

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