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Student[MultivariateCalculus]

 Contains
 test if a point is on a line or a plane, or a line is embedded in a plane

 Calling Sequence Contains(pl1, pl2)

Parameters

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

Returns

 • truefalse ; whether the first argument contains the second argument

Description

 • The Contains command tests if all of the points in the second object are in the first object. Typically, it tests if a Line or Plane contains a given point, or if a Plane contains a given Line.

Examples

 > $\mathrm{with}\left({\mathrm{Student}}_{\mathrm{MultivariateCalculus}}\right):$
 > $\mathrm{l1}≔\mathrm{Line}\left(\left[0,4,2\right],⟨1,1,1⟩\right):$
 > $\mathrm{Contains}\left(\mathrm{l1},\left[1,5,3\right]\right)$
 ${\mathrm{true}}$ (1)
 > $\mathrm{Contains}\left(\mathrm{l1},\left[0,0,0\right]\right)$
 ${\mathrm{false}}$ (2)
 > $\mathrm{p1}≔\mathrm{Plane}\left(\left[0,4,2\right],\left[5,9,7\right],\left[-1,6,3\right]\right):$
 > $\mathrm{Contains}\left(\mathrm{p1},\mathrm{l1}\right)$
 ${\mathrm{true}}$ (3)
 > $\mathrm{Contains}\left(\mathrm{p1},\left[0,0,0\right]\right)$
 ${\mathrm{false}}$ (4)

Line l2 is not embedded in the Plane p1 because they intersect in a point only.

 > $\mathrm{l2}≔\mathrm{Line}\left(\left[0,1,-1\right],⟨4,2,6⟩\right):$
 > $\mathrm{Contains}\left(\mathrm{p1},\mathrm{l2}\right)$
 ${\mathrm{false}}$ (5)
 > $\mathrm{GetIntersection}\left(\mathrm{l2},\mathrm{p1}\right)$
 $\left[\frac{{6}}{{5}}{,}\frac{{8}}{{5}}{,}\frac{{4}}{{5}}\right]$ (6)

Compatibility

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