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geom3d

 parallel
 return the line or plane passing through a given point or line that is parallel to a given line or plane

 Calling Sequence parallel(w, u, v)

Parameters

 w - name of the object to be created u - point or a line v - line or plane; v can be a plane only if u is a point

Description

 • If u is a point and v is a line (or plane), the parallel(w, u, v) function defines w as the line (or plane) that passes through u and is parallel to v.
 • If u is a line, and v is a line, the parallel(w, u, v) function defines w as the plane that contains u and is parallel to v.
 • Use the function geom3d[detail] for more details about the created object.
 • The command with(geom3d,parallel) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{geom3d}\right):$
 > $\mathrm{point}\left(A,0,0,0\right),\mathrm{point}\left(B,1,0,0\right),\mathrm{point}\left(C,0,1,0\right),\mathrm{point}\left(F,0,0,1\right):$
 > $\mathrm{plane}\left(p,x+y+z=1,\left[x,y,z\right]\right),\mathrm{line}\left(\mathrm{A_B},\left[A,B\right]\right),\mathrm{line}\left(\mathrm{C_F},\left[C,F\right]\right):$
 > $\mathrm{parallel}\left(\mathrm{p1},A,p\right):$
 > $\mathrm{detail}\left(\mathrm{p1}\right)$
 $\begin{array}{ll}{\text{name of the object}}& {\mathrm{p1}}\\ {\text{form of the object}}& {\mathrm{plane3d}}\\ {\text{equation of the plane}}& {x}{+}{y}{+}{z}{=}{0}\end{array}$ (1)
 > $\mathrm{parallel}\left(\mathrm{p2},\mathrm{A_B},\mathrm{C_F}\right):$
 > $\mathrm{detail}\left(\mathrm{p2}\right)$
 $\begin{array}{ll}{\text{name of the object}}& {\mathrm{p2}}\\ {\text{form of the object}}& {\mathrm{plane3d}}\\ {\text{equation of the plane}}& {-}{y}{-}{z}{=}{0}\end{array}$ (2)