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Student[MultivariateCalculus]

 GetIntersection
 obtain the intersection of lines or planes

 Calling Sequence GetIntersection(pl1, pl2)

Parameters

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

Returns

 • the empty set, $\left\{\right\}$, 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.

Description

 • 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 $\left\{\right\}$, 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 $A$.

Examples

 > $\mathrm{with}\left(\mathrm{Student}[\mathrm{MultivariateCalculus}]\right):$
 > $\mathrm{l1}≔\mathrm{Line}\left(\left[0,2,6\right],⟨10,15,20⟩\right):$
 > $\mathrm{l2}≔\mathrm{Line}\left(\left[-3,7,3\right],⟨2,3,4⟩\right):$
 > $\mathrm{AreParallel}\left(\mathrm{l1},\mathrm{l2}\right)$
 ${\mathrm{true}}$ (1)
 > $\mathrm{Intersects}\left(\mathrm{l1},\mathrm{l2}\right)$
 ${\mathrm{false}}$ (2)
 > $\mathrm{GetIntersection}\left(\mathrm{l1},\mathrm{l2}\right)$
 $\left\{{}\right\}$ (3)
 > $\mathrm{p1}≔\mathrm{Plane}\left(\left[0,3,1\right],⟨0,3,2⟩\right):$
 > $\mathrm{p2}≔\mathrm{Plane}\left(\left[-4,1,3\right],⟨0,3,2⟩\right):$
 > $\mathrm{Intersects}\left(\mathrm{p1},\mathrm{p2}\right)$
 ${\mathrm{false}}$ (4)
 > $\mathrm{GetIntersection}\left(\mathrm{p1},\mathrm{p2}\right)$
 $\left\{{}\right\}$ (5)
 > $\mathrm{Intersects}\left(\mathrm{p1},\mathrm{l2}\right)$
 ${\mathrm{true}}$ (6)
 > $\mathrm{GetIntersection}\left(\mathrm{p1},\mathrm{l2}\right)$
 $\left[{-}\frac{{83}}{{17}}{,}\frac{{71}}{{17}}{,}{-}\frac{{13}}{{17}}\right]$ (7)
 > $\mathrm{Intersects}\left(\mathrm{l1},\mathrm{p2}\right)$
 ${\mathrm{true}}$ (8)
 > $\mathrm{GetIntersection}\left(\mathrm{p2},\mathrm{l1}\right)$
 $\left[{-}\frac{{18}}{{17}}{,}\frac{{7}}{{17}}{,}\frac{{66}}{{17}}\right]$ (9)
 > $\mathrm{p3}≔\mathrm{Plane}\left(\left[0,0,0\right],⟨3,3,1⟩\right):$
 > $\mathrm{Intersects}\left(\mathrm{p1},\mathrm{p3}\right)$
 ${\mathrm{true}}$ (10)
 > $\mathrm{l3}≔\mathrm{GetIntersection}\left(\mathrm{p1},\mathrm{p3}\right):$
 > $\mathrm{GetDirection}\left(\mathrm{l3}\right)$
 $\left[\begin{array}{r}{-}{3}\\ {6}\\ {-}{9}\end{array}\right]$ (11)
 > $\mathrm{GetPoint}\left(\mathrm{l3}\right)$
 $\left[{-}\frac{{121}}{{42}}{,}\frac{{44}}{{21}}{,}\frac{{33}}{{14}}\right]$ (12)

Compatibility

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