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.

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

$\mathrm{l1}≔\mathrm{Line}\left(\left[0\,2\right]\,⟨1\,1⟩\right)\:$

$\mathrm{l2}≔\mathrm{Line}\left(\left[1\,2\right]\,⟨1\,-1⟩\right)\:$

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

$\mathrm{true}$

$\mathrm{l3}≔\mathrm{Line}\left(\left[0\,2\,1\right]\,⟨2\,3\,2⟩\right)\:$

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

$\mathrm{AreOrthogonal}\left(\mathrm{l3}\,\mathrm{l4}\right)$

$\mathrm{true}$

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

$\mathrm{AreOrthogonal}\left(\mathrm{l3}\,\mathrm{l5}\right)$

$\mathrm{false}$

$\mathrm{p1}≔\mathrm{Plane}\left(\left[8\,2\,6\right]\,⟨2\,12\,-8⟩\right)\:$

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

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

$\mathrm{false}$

$\mathrm{p3}≔\mathrm{Plane}\left(\left[0\,0\,0\right]\,⟨-24\,10\,9⟩\right)\:$

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

$\mathrm{true}$

$\mathrm{AreOrthogonal}\left(\mathrm{l3}\,\mathrm{p3}\right)$

$\mathrm{false}$

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

For more information on Maple 18 changes, see Updates in Maple 18.