The Intersects command determines if two Line or Plane objects intersect.

The point, line, or plane of intersection can be obtained by GetIntersection.

Two Line objects in 3D can be non-parallel but non-intersecting.  Such two lines are skew.  This property can be detected by AreSkew.

If one object is contained in another object, then they intersect. In particular, if two objects are equal, then they intersect.

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

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

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

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

$\mathrm{true}$

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

$\mathrm{false}$

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

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

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

$\mathrm{false}$

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

$\mathrm{true}$

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

$\mathrm{true}$

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

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