Intersects - Maple Help

Student[MultivariateCalculus]

 Intersects
 test if lines or planes intersect

 Calling Sequence Intersects(pl1, pl2)

Parameters

 pl1, pl2 - list, Line, Plane ; point, Line or Plane defined by Student[MultivariateCalculus].

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{Student}\left[\mathrm{MultivariateCalculus}\right]\right):$
 > $\mathrm{l1}≔\mathrm{Line}\left(\left[0,2,6\right],⟨10,15,20⟩\right):$
 > $\mathrm{l2}≔\mathrm{Line}\left(\left[-3,7,3\right],⟨2,3,4⟩\right):$
 > $\mathrm{AreParallel}\left(\mathrm{l1},\mathrm{l2}\right)$
 ${\mathrm{true}}$ (1)
 > $\mathrm{Intersects}\left(\mathrm{l1},\mathrm{l2}\right)$
 ${\mathrm{false}}$ (2)
 > $\mathrm{p1}≔\mathrm{Plane}\left(\left[0,3,1\right],⟨0,3,2⟩\right):$
 > $\mathrm{p2}≔\mathrm{Plane}\left(\left[-4,1,3\right],⟨0,3,2⟩\right):$
 > $\mathrm{Intersects}\left(\mathrm{p1},\mathrm{p2}\right)$
 ${\mathrm{false}}$ (3)
 > $\mathrm{Intersects}\left(\mathrm{p1},\mathrm{l2}\right)$
 ${\mathrm{true}}$ (4)
 > $\mathrm{Intersects}\left(\mathrm{l1},\mathrm{p2}\right)$
 ${\mathrm{true}}$ (5)

Compatibility

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