The Distance command calculates the distance between two lines, planes or points.

If the arguments intersect, the Distance command returns zero.

The answer is not necessarily simplified. The command evalf can be used to convert the answer to a floating point value.

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

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

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

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

$\mathrm{true}$

$d≔\mathrm{Distance}\left(\mathrm{l1}\,\mathrm{l2}\right)$

$d≔\frac{\sqrt{1238}\sqrt{29}}{29}$

$\mathrm{evalf}\left(d\right)$

$6.533732100$

$\mathrm{Distance}\left(\mathrm{l1}\,\left[-5\,-6\,2\right]\right)$

$\frac{\sqrt{545}\sqrt{29}}{29}$

$\mathrm{l3}≔\mathrm{Line}\left(\left[-3\,7\,3\right]\,\left[7\,1\,6\right]\right)\:$

$\mathrm{Intersects}\left(\mathrm{l2}\,\mathrm{l3}\right)$

$\mathrm{true}$

$\mathrm{Distance}\left(\mathrm{l2}\,\mathrm{l3}\right)$

$0$

$\mathrm{l4}≔\mathrm{Line}\left(\left[5\,2\right]\,⟨9\,-2⟩\right)\:$

$\mathrm{l5}≔\mathrm{Line}\left(\left[0\,0\right]\,⟨9\,-2⟩\right)\:$

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

$\frac{28\sqrt{85}}{85}$

$\mathrm{p1}≔\mathrm{Plane}\left(\left[1\,0\,0\right]\,\left[0\,2\,0\right]\,\left[0\,0\,3\right]\right)\:$

$\mathrm{Distance}\left(\mathrm{p1}\,\left[2\,3\,4\right]\right)$

$\frac{23}{7}$

$\mathrm{p2}≔\mathrm{Plane}\left(10x+2y-2z=5\right)\:$

$\mathrm{p3}≔\mathrm{Plane}\left(5x+y-z=1\right)\:$

$\mathrm{Distance}\left(\mathrm{p2}\,\mathrm{p3}\right)$

$\frac{\sqrt{3}}{6}$

$\mathrm{l6}≔\mathrm{Line}\left(\left[-2\,3\,-10\right]\,⟨7\,0\,0⟩\right)\:$

$\mathrm{p2}≔\mathrm{Plane}\left(\left[3\,6\,1\right]\,⟨0\,0\,7⟩\right)\:$

$\mathrm{Intersects}\left(\mathrm{p2}\,\mathrm{l6}\right)$

$\mathrm{false}$

$\mathrm{Distance}\left(\mathrm{p2}\,\mathrm{l6}\right)$

$11$

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

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