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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.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{MultivariateCalculus}\right]\right)\:$

$\mathrm{l1}≔\mathrm{Line}\left(\left[0\,2\,6\right]\,⟨10\,15\,20⟩\right)\:$

$\mathrm{l2}≔\mathrm{Line}\left(\left[-3\,7\,3\right]\,⟨2\,3\,4⟩\right)\:$

$\mathrm{AreParallel}\left(\mathrm{l1}\,\mathrm{l2}\right)$

$\mathrm{true}$

$\mathrm{l3}≔\mathrm{Line}\left(\left[3\,2\,3\right]\,⟨-2\,6\,1⟩\right)\:$

$\mathrm{AreParallel}\left(\mathrm{l1}\,\mathrm{l3}\right)$

$\mathrm{false}$

$\mathrm{l4}≔\mathrm{Line}\left(\left[0\,-1\,-2\right]\,⟨1\,2\,3⟩\right)\:$

$\mathrm{l5}≔\mathrm{Line}\left(\left[-3\,-2\,-1\right]\,⟨-4\,-3\,2⟩\right)\:$

$\mathrm{AreParallel}\left(\mathrm{l4}\,\mathrm{l5}\right)$

$\mathrm{false}$

$\mathrm{Intersects}\left(\mathrm{l4}\,\mathrm{l5}\right)$

$\mathrm{false}$

$\mathrm{AreSkew}\left(\mathrm{l4}\,\mathrm{l5}\right)$

$\mathrm{true}$

$\mathrm{l6}≔\mathrm{Line}\left(\left[-1\,-3\right]\,\left[4\,5\right]\right)\:$

$\mathrm{l7}≔\mathrm{Line}\left(\left[0\,8\right]\,⟨5\,8⟩\right)\:$

$\mathrm{AreParallel}\left(\mathrm{l6}\,\mathrm{l7}\right)$

$\mathrm{true}$

$\mathrm{p1}≔\mathrm{Plane}\left(\left[8\,2\,6\right]\,⟨-1\,-6\,4⟩\right)\:$

$\mathrm{p2}≔\mathrm{Plane}\left(\left[-2\,8\,-6\right]\,⟨1\,6\,-4⟩\right)\:$

$\mathrm{AreParallel}\left(\mathrm{p1}\,\mathrm{p2}\right)$

$\mathrm{true}$

$\mathrm{p3}≔\mathrm{Plane}\left(\left[3\,7\,1\right]\,\left[7\,1\,3\right]\,\left[-3\,6\,-10\right]\right)\:$

$\mathrm{AreParallel}\left(\mathrm{p1}\,\mathrm{p3}\right)$

$\mathrm{false}$

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

For more information on Maple 17 changes, see Updates in Maple 17 .