 Student[MultivariateCalculus] - Maple Programming Help

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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

 > with(Student[MultivariateCalculus]):
 > l1 := Line([0,4,2], <1,1,1>):
 > Contains(l1, [1,5,3]);
 ${\mathrm{true}}$ (1)
 > Contains(l1, [0,0,0]);
 ${\mathrm{false}}$ (2)
 > p1 := Plane([0,4,2], [5,9,7], [-1,6,3]):
 > Contains(p1, l1);
 ${\mathrm{true}}$ (3)
 > Contains(p1, [0,0,0]);
 ${\mathrm{false}}$ (4)

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

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

Compatibility

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