A plane p can be defined as follows:

from three given points A, B, and C.

from a given point A and a vector of dimension 3 v or a directed segment dseg. The plane defined is the plane that passes through A and has v or dseg as one of its normal vectors.

from two directed line segments with the same tail dseg1 and dseg2.

from two given lines l1 and l2. If l1 and l2 are parallel or intersect each other, the plane defined is the one that contains both l1 and l2. And if l1 and l2 are skew lines, p is the plane that contains l1 and is parallel to l2.

from a point A and two lines l1 and l2. The plane defined is the one that passes through A and is parallel to two lines l1 and l2.

from its algebraic representation eqn, i.e., eqn is a polynomial or an equation. In case the third optional argument is not given, if names are assigned to the three environment variables _EnvXName, _EnvYName, and _EnvZName then these three names will be used as the names of the axes.  Otherwise, Maple will prompt the user to input the names of the axes.

To access the information relating to a plane p, use the following function calls:

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

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

$\mathrm{plane}\left(\mathrm{p1}\,x-y+4z=1\,\left[x\,y\,z\right]\right)\:$$\mathrm{plane}\left(\mathrm{p2}\,2x+y-3z=2\,\left[x\,y\,z\right]\right)\:$

$\mathrm{line}\left(\mathrm{l1}\,\left[\mathrm{p1}\,\mathrm{p2}\right]\right)\:$

$\mathrm{line}\left(\mathrm{l2}\,\left[\mathrm{point}\left(A\,-3\,-\frac{1}{2}\,-\frac{2}{3}\right)\,\left[1\,\frac{1}{2}\,\frac{1}{3}\right]\right]\right)\:$

$\mathrm{point}\left(o\,0\,0\,0\right)\:$

$\mathrm{plane}\left(p\,\left[o\,\mathrm{l1}\,\mathrm{l2}\right]\right)$

$p$

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

$\begin{array}{ll}\text{name of the object}& p\\ \text{form of the object}& \mathrm{plane3d}\\ \text{equation of the plane}& \frac{13x}{6}+\frac{10y}{3}-\frac{23z}{2}=0\end{array}$

$\mathrm{assume}\left(\mathrm{x1}\ne \mathrm{x2}\right)\:$

$\mathrm{point}\left(A\,\mathrm{x1}\,\mathrm{y1}\,\mathrm{z1}\right),\mathrm{point}\left(B\,\mathrm{x2}\,\mathrm{y2}\,\mathrm{z2}\right)\:$

$\mathrm{midpoint}\left(C\,A\,B\right)\:$$\mathrm{line}\left(l\,\left[A\,B\right]\right)\:$

$v≔\mathrm{ParallelVector}\left(l\right)\:$

$\mathrm{plane}\left(p\,\left[C\,v\right]\right)$

$p$

$\mathrm{Equation}\left(p\,\left[x\,y\,z\right]\right)$

$x\left(\mathrm{x2~}-\mathrm{x1~}\right)+y\left(\mathrm{y2}-\mathrm{y1}\right)+z\left(\mathrm{z2}-\mathrm{z1}\right)-\left(\mathrm{x2~}-\mathrm{x1~}\right)\left(\frac{\mathrm{x1~}}{2}+\frac{\mathrm{x2~}}{2}\right)-\left(\mathrm{y2}-\mathrm{y1}\right)\left(\frac{\mathrm{y1}}{2}+\frac{\mathrm{y2}}{2}\right)-\left(\mathrm{z2}-\mathrm{z1}\right)\left(\frac{\mathrm{z1}}{2}+\frac{\mathrm{z2}}{2}\right)=0$