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geom3d

 projection
 find the projection of an object on the other object

 Calling Sequence projection(Q, A, l) projection(Q, A, p) projection(Q, seg, p) projection(Q, l, p)

Parameters

 Q - the name of the object to be created A - point seg - line segment or a directed line segment l - line p - plane

Description

 • The routine finds the projection Q of an object on the other object.
 • For a detailed description of the object to be created Q, use the routine detail (e.g., detail(Q))
 • The command with(geom3d,projection) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{geom3d}\right):$

Find the equations of the projection of the line $\frac{1}{2}x-\frac{1}{2}=-y-1$=$\frac{1}{4}z-\frac{3}{4}$ on the plane $x+2y+z$=6

 > $\mathrm{line}\left(l,\left[\mathrm{point}\left(o,1,-1,3\right),\left[2,-1,4\right]\right]\right):$
 > $\mathrm{plane}\left(p,x+2y+z=6,\left[x,y,z\right]\right):$
 > $\mathrm{projection}\left(\mathrm{l1},l,p\right)$
 ${\mathrm{l1}}$ (1)
 > $\mathrm{detail}\left(\mathrm{l1}\right)$
 Warning, assume that the parameter in the parametric equations is _t Warning, assuming that the names of the axes are _x, _y, and _z
 $\begin{array}{ll}{\text{name of the object}}& {\mathrm{l1}}\\ {\text{form of the object}}& {\mathrm{line3d}}\\ {\text{equation of the line}}& \left[{\mathrm{_x}}{=}\frac{{5}}{{3}}{+}\frac{{4}{}{\mathrm{_t}}}{{3}}{,}{\mathrm{_y}}{=}\frac{{1}}{{3}}{-}\frac{{7}{}{\mathrm{_t}}}{{3}}{,}{\mathrm{_z}}{=}\frac{{11}}{{3}}{+}\frac{{10}{}{\mathrm{_t}}}{{3}}\right]\end{array}$ (2)