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Student[MultivariateCalculus]

 AreParallel
 test if lines or planes are parallel

 Calling Sequence AreParallel(l1, l2) AreParallel(p1, p2) AreParallel(l1, p1) AreParallel(p1, l1)

Parameters

 l1, l2 - Line; Line defined in Student[MultivariateCalculus] p1, p2 - Plane; Plane defined in Student[MultivariateCalculus]

Description

 • The AreParallel command determines if two lines or two planes are parallel or not, or if a line and a plane are parallel.
 • The Line can be either in 2D or 3D.
 • Two Line objects in 3D can be non-intersecting but not parallel to each other.  This property between such lines, which is called skewness, can be detected using AreSkew.
 • Two identical lines or two identical planes are parallel to each other. Similarly, a line that lies in a plane is parallel to that plane.

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)
 > $\mathrm{l3}≔\mathrm{Line}\left(\left[3,2,3\right],⟨-2,6,1⟩\right):$
 > $\mathrm{AreParallel}\left(\mathrm{l1},\mathrm{l3}\right)$
 ${\mathrm{false}}$ (2)
 > $\mathrm{l4}≔\mathrm{Line}\left(\left[0,-1,-2\right],⟨1,2,3⟩\right):$
 > $\mathrm{l5}≔\mathrm{Line}\left(\left[-3,-2,-1\right],⟨-4,-3,2⟩\right):$
 > $\mathrm{AreParallel}\left(\mathrm{l4},\mathrm{l5}\right)$
 ${\mathrm{false}}$ (3)
 > $\mathrm{Intersects}\left(\mathrm{l4},\mathrm{l5}\right)$
 ${\mathrm{false}}$ (4)
 > $\mathrm{AreSkew}\left(\mathrm{l4},\mathrm{l5}\right)$
 ${\mathrm{true}}$ (5)
 > $\mathrm{l6}≔\mathrm{Line}\left(\left[-1,-3\right],\left[4,5\right]\right):$
 > $\mathrm{l7}≔\mathrm{Line}\left(\left[0,8\right],⟨5,8⟩\right):$
 > $\mathrm{AreParallel}\left(\mathrm{l6},\mathrm{l7}\right)$
 ${\mathrm{true}}$ (6)
 > $\mathrm{p1}≔\mathrm{Plane}\left(\left[8,2,6\right],⟨-1,-6,4⟩\right):$
 > $\mathrm{p2}≔\mathrm{Plane}\left(\left[-2,8,-6\right],⟨1,6,-4⟩\right):$
 > $\mathrm{AreParallel}\left(\mathrm{p1},\mathrm{p2}\right)$
 ${\mathrm{true}}$ (7)
 > $\mathrm{p3}≔\mathrm{Plane}\left(\left[3,7,1\right],\left[7,1,3\right],\left[-3,6,-10\right]\right):$
 > $\mathrm{AreParallel}\left(\mathrm{p1},\mathrm{p3}\right)$
 ${\mathrm{false}}$ (8)

Compatibility

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