A line l can be defined as follows:

+ from two given points A and B

+ from a given point A and a vector v of dimension 3 or a directed segment seg. The line defined is the line that passes through A and has v as its direction-ratios.

+ from a given point A and a plane p1. The line defined is the line that passes through A and perpendicular to the plane p1.

+ from two given planes p1 and p2. The line defined is the line of intersection of two planes p1 and p2 (if exists).

+ from the parametric equations of the line $\left[\mathrm{b1}t+\mathrm{a1}\,\mathrm{b2}t+\mathrm{a2}\,\mathrm{b3}t+\mathrm{a3}\right]$. If the third optional argument t is not given, and if a name is assigned to the environment variable _EnvTName, then this name will be used as the name of the parameter in the parametric equations of the line. Otherwise, Maple will prompt the user to input the name of the parameter.

To access the information relating to a line l, use the following function calls:

The command with(geom3d,line) allows the use of the abbreviated form of this command.

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

$\mathrm{point}\left(A\,1\,2\,-1\right),\mathrm{plane}\left(p\,3x-5y+4z=5\,\left[x\,y\,z\right]\right)\:$

$\mathrm{line}\left(l\,\left[A\,p\right]\right)$

$l$

$\mathrm{Equation}\left(l\,'t'\right)$

$\left[1+3t\,2-5t\,-1+4t\right]$

$\mathrm{projection}\left(B\,A\,p\right)$

$B$

$\mathrm{coordinates}\left(B\right)$

$\left[\frac{49}{25}\,\frac{2}{5}\,\frac{7}{25}\right]$

$\mathrm{distance}\left(A\,B\right)$

$\frac{8\sqrt{2}}{5}$

$\mathrm{assume}\left(l\ne 0\right)\:$

$\mathrm{point}\left(A\,\left[\mathrm{x1}\,\mathrm{y1}\,\mathrm{z1}\right]\right)\:$$v≔\left[l\,m\,n\right]\:$

$\mathrm{line}\left(\mathrm{l1}\,\left[A\,v\right]\right)\:$

$\mathrm{detail}\left(\mathrm{l1}\right)$

$\begin{array}{ll}\text{name of the object}& \mathrm{l1}\\ \text{form of the object}& \mathrm{line3d}\\ \text{equation of the line}& \left[\mathrm{\_x}=\mathrm{\_t}\mathrm{l~}+\mathrm{x1}\,\mathrm{\_y}=\mathrm{\_t}m+\mathrm{y1}\,\mathrm{\_z}=\mathrm{\_t}n+\mathrm{z1}\right]\end{array}$

$l≔'l'\:$

$\mathrm{plane}\left(\mathrm{p1}\,4x+4y-5z=12\,\left[x\,y\,z\right]\right)\:$

$\mathrm{plane}\left(\mathrm{p2}\,8x+12y-13z=32\,\left[x\,y\,z\right]\right)\:$

$\mathrm{line}\left(l\,\left[\mathrm{p1}\,\mathrm{p2}\right]\right)$

$l$

$\mathrm{Equation}\left(l\,'t'\right)$

$\left[1+8t\,2+12t\,16t\right]$