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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 .