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geom3d

 Equation
 equation of a geometric object

 Calling Sequence Equation(obj) Equation(obj, t ) Equation(obj, [x,y,z] )

Parameters

 obj - the given geometric object t - (optional) the name of the parameter in the parametric equations of a line [x, y, z] - (optional) the names of the axes

Description

 • The routine returns an algebraic representation of the given geometric object.
 • Users will be asked to provide the names of the axes or the name of the parameter in the parametric equations (when obj is a line) if they are not assigned to names and if the second optional argument is not given.  See xname for an example of this.
 • The command with(geom3d,Equation) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{geom3d}\right):$
 > $\mathrm{point}\left(A,0,0,0\right),\mathrm{point}\left(B,1,2,3\right):$

Define the line that passes through two points A and B

 > $\mathrm{line}\left(l,\left[A,B\right]\right)$
 ${l}$ (1)

The equation of l is:

 > $\mathrm{Equation}\left(l,m\right)$
 $\left[{m}{,}{2}{}{m}{,}{3}{}{m}\right]$ (2)
 > $\mathrm{point}\left(C,3,7,11\right):$

Define the plane that passes through three given points A, B, C

 > $\mathrm{plane}\left(p,\left[A,B,C\right],\left[a,b,c\right]\right):$
 > $\mathrm{Equation}\left(p\right)$
 ${a}{-}{2}{}{b}{+}{c}{=}{0}$ (3)