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Student[MultivariateCalculus]

 AreSkew
 determine if two lines are skew

 Calling Sequence AreSkew(l1, l2)

Parameters

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

Description

 • The AreSkew command determines if two Line objects are skew.
 • Lines are skew if they do not intersect and are not parallel to each other. Since lines in 2D space always either intersect or are parallel, this command always returns false for lines in 2D space.

Examples

 > $\mathrm{with}\left(\mathrm{Student}\left[\mathrm{MultivariateCalculus}\right]\right):$
 > $\mathrm{l1}≔\mathrm{Line}\left(\left[3,2,6\right],⟨-2,5,1⟩\right):$
 > $\mathrm{l2}≔\mathrm{Line}\left(\left[5,7,3\right],⟨4,2,2⟩\right):$
 > $\mathrm{AreSkew}\left(\mathrm{l1},\mathrm{l2}\right)$
 ${\mathrm{true}}$ (1)
 > $\mathrm{Intersects}\left(\mathrm{l1},\mathrm{l2}\right)$
 ${\mathrm{false}}$ (2)
 > $\mathrm{AreParallel}\left(\mathrm{l1},\mathrm{l2}\right)$
 ${\mathrm{false}}$ (3)

Graphing two skew lines.

 > $\mathrm{p1}≔\mathrm{GetPlot}\left(\mathrm{Line}\left(\left[3,2,6\right],⟨-2,5,1⟩\right),'\mathrm{caption}'="",'\mathrm{showvector}'=\mathrm{false},'\mathrm{showpoint}'=\mathrm{false},'\mathrm{lineoptions}'=\left['\mathrm{color}'="red"\right]\right):$
 > $\mathrm{p2}≔\mathrm{GetPlot}\left(\mathrm{Line}\left(\left[5,7,3\right],⟨4,2,2⟩\right),'\mathrm{caption}'="",'\mathrm{showvector}'=\mathrm{false},'\mathrm{showpoint}'=\mathrm{false},'\mathrm{lineoptions}'=\left['\mathrm{color}'="green"\right]\right):$
 > $\mathrm{plots}\left[\mathrm{display}\right]\left(\left[\mathrm{p1},\mathrm{p2}\right],'\mathrm{caption}'="Two skew lines"\right)$
 > $\mathrm{l3}≔\mathrm{Line}\left(\left[0,1,0\right],⟨6,9,-3⟩\right):$
 > $\mathrm{l4}≔\mathrm{Line}\left(\left[1,4,0\right],⟨-2,-3,1⟩\right):$
 > $\mathrm{AreSkew}\left(\mathrm{l3},\mathrm{l4}\right)$
 ${\mathrm{false}}$ (4)
 > $\mathrm{Intersects}\left(\mathrm{l3},\mathrm{l4}\right)$
 ${\mathrm{false}}$ (5)
 > $\mathrm{AreParallel}\left(\mathrm{l3},\mathrm{l4}\right)$
 ${\mathrm{true}}$ (6)

Graphing two parallel lines.

 > $\mathrm{p3}≔\mathrm{GetPlot}\left(\mathrm{Line}\left(\left[0,1,0\right],⟨6,9,-3⟩\right),'\mathrm{caption}'="",'\mathrm{showvector}'=\mathrm{false},'\mathrm{showpoint}'=\mathrm{false},'\mathrm{lineoptions}'=\left['\mathrm{color}'="red"\right]\right):$
 > $\mathrm{p4}≔\mathrm{GetPlot}\left(\mathrm{Line}\left(\left[1,4,0\right],⟨-2,-3,1⟩\right),'\mathrm{caption}'="",'\mathrm{showvector}'=\mathrm{false},'\mathrm{showpoint}'=\mathrm{false},'\mathrm{lineoptions}'=\left['\mathrm{color}'="green"\right]\right):$
 > $\mathrm{plots}\left[\mathrm{display}\right]\left(\left[\mathrm{p3},\mathrm{p4}\right],'\mathrm{caption}'="Two parallel lines"\right)$

Compatibility

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