the empty set, $\varnothing$, if the lines or planes don't intersect.

a list of coordinate values, if the intersection is a point.

a Line or Plane object, if that is the intersection.

The GetIntersection command obtains the intersection of two point, Line, or Plane objects as understood by the Student[MultivariateCalculus] package.

The Intersects command can be used to test if lines and/or planes intersect.

The empty set, denoted by $\varnothing$, is returned if the lines or planes do not intersect.

If one object is contained in another, then their intersection is the smaller object. In particular, the intersection of any object $A$ with itself is that object $A$.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{MultivariateCalculus}\right]\right)\:$

$\mathrm{l1}≔\mathrm{Line}\left(\left[0\,2\,6\right]\,⟨10\,15\,20⟩\right)\:$

$\mathrm{l2}≔\mathrm{Line}\left(\left[-3\,7\,3\right]\,⟨2\,3\,4⟩\right)\:$

$\mathrm{AreParallel}\left(\mathrm{l1}\,\mathrm{l2}\right)$

$\mathrm{true}$

$\mathrm{Intersects}\left(\mathrm{l1}\,\mathrm{l2}\right)$

$\mathrm{false}$

$\mathrm{GetIntersection}\left(\mathrm{l1}\,\mathrm{l2}\right)$

$\varnothing$

$\mathrm{p1}≔\mathrm{Plane}\left(\left[0\,3\,1\right]\,⟨0\,3\,2⟩\right)\:$

$\mathrm{p2}≔\mathrm{Plane}\left(\left[-4\,1\,3\right]\,⟨0\,3\,2⟩\right)\:$

$\mathrm{Intersects}\left(\mathrm{p1}\,\mathrm{p2}\right)$

$\mathrm{false}$

$\mathrm{GetIntersection}\left(\mathrm{p1}\,\mathrm{p2}\right)$

$\varnothing$

$\mathrm{Intersects}\left(\mathrm{p1}\,\mathrm{l2}\right)$

$\mathrm{true}$

$\mathrm{GetIntersection}\left(\mathrm{p1}\,\mathrm{l2}\right)$

$\left[-\frac{83}{17}\,\frac{71}{17}\,-\frac{13}{17}\right]$

$\mathrm{Intersects}\left(\mathrm{l1}\,\mathrm{p2}\right)$

$\mathrm{true}$

$\mathrm{GetIntersection}\left(\mathrm{p2}\,\mathrm{l1}\right)$

$\left[-\frac{18}{17}\,\frac{7}{17}\,\frac{66}{17}\right]$

$\mathrm{p3}≔\mathrm{Plane}\left(\left[0\,0\,0\right]\,⟨3\,3\,1⟩\right)\:$

$\mathrm{Intersects}\left(\mathrm{p1}\,\mathrm{p3}\right)$

$\mathrm{true}$

$\mathrm{l3}≔\mathrm{GetIntersection}\left(\mathrm{p1}\,\mathrm{p3}\right)\:$

$\mathrm{GetDirection}\left(\mathrm{l3}\right)$

$\left[\begin{array}{c}\mathrm{-3}\\ 6\\ \mathrm{-9}\end{array}\right]$

$\mathrm{GetPoint}\left(\mathrm{l3}\right)$

$\left[-\frac{121}{42}\,\frac{44}{21}\,\frac{33}{14}\right]$

The Student[MultivariateCalculus][GetIntersection] command was introduced in Maple 17.

For more information on Maple 17 changes, see Updates in Maple 17.