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Student[MultivariateCalculus]

 AreOrthogonal
 test if lines or planes are orthogonal

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

Parameters

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

Description

 • The AreOrthogonal command determines if two lines or two planes are orthogonal or not, or if a line and a plane are orthogonal.
 • The Line can be either in 2D or 3D.

Examples

 > $\mathrm{with}\left(\mathrm{Student}\left[\mathrm{MultivariateCalculus}\right]\right):$
 > $\mathrm{l1}≔\mathrm{Line}\left(\left[0,2\right],⟨1,1⟩\right):$
 > $\mathrm{l2}≔\mathrm{Line}\left(\left[1,2\right],⟨1,-1⟩\right):$
 > $\mathrm{AreOrthogonal}\left(\mathrm{l1},\mathrm{l2}\right)$
 ${\mathrm{true}}$ (1)
 > $\mathrm{l3}≔\mathrm{Line}\left(\left[0,2,1\right],⟨2,3,2⟩\right):$
 > $\mathrm{l4}≔\mathrm{Line}\left(\left[1,2,3\right],⟨-3,2,0⟩\right):$
 > $\mathrm{AreOrthogonal}\left(\mathrm{l3},\mathrm{l4}\right)$
 ${\mathrm{true}}$ (2)
 > $\mathrm{l5}≔\mathrm{Line}\left(\left[3,2,3\right],⟨2,3,2⟩\right):$
 > $\mathrm{AreOrthogonal}\left(\mathrm{l3},\mathrm{l5}\right)$
 ${\mathrm{false}}$ (3)
 > $\mathrm{p1}≔\mathrm{Plane}\left(\left[8,2,6\right],⟨2,12,-8⟩\right):$
 > $\mathrm{p2}≔\mathrm{Plane}\left(\left[-2,8,-6\right],⟨1,6,-4⟩\right):$
 > $\mathrm{AreOrthogonal}\left(\mathrm{p1},\mathrm{p2}\right)$
 ${\mathrm{false}}$ (4)
 > $\mathrm{p3}≔\mathrm{Plane}\left(\left[0,0,0\right],⟨-24,10,9⟩\right):$
 > $\mathrm{AreOrthogonal}\left(\mathrm{p1},\mathrm{p3}\right)$
 ${\mathrm{true}}$ (5)
 > $\mathrm{AreOrthogonal}\left(\mathrm{l3},\mathrm{p3}\right)$
 ${\mathrm{false}}$ (6)

Compatibility

 • The Student[MultivariateCalculus][AreOrthogonal] command was introduced in Maple 18.