GetPoint - Maple Help

Student[MultivariateCalculus]

 GetPoint
 obtain an arbitrary point in a line or plane

 Calling Sequence GetPoint(l) GetPoint(p)

Parameters

 l - Line ; Line defined in Student[MultivariateCalculus] p - Plane ; Plane defined in Student[MultivariateCalculus]

Returns

 • list ; A point on a line or plane

Description

 • The GetPoint command returns an arbitrary point on a line or plane.
 • This command guarantees that the point returned lies on the line or the plane, but it does not guarantee the location of the point relative to the axis, the origin, or any points provided to Line or Plane constructors.

Examples

 > $\mathrm{with}\left({\mathrm{Student}}_{\mathrm{MultivariateCalculus}}\right):$
 > $l≔\mathrm{Line}\left(\left[1,5,2\right],\left[3,2,2\right]\right):$
 > $\mathrm{GetPoint}\left(l\right)$
 $\left[{1}{,}{5}{,}{2}\right]$ (1)
 > $\mathrm{Contains}\left(l,\left[1,5,2\right]\right)$
 ${\mathrm{true}}$ (2)

The point $\left[\frac{24}{139},-\frac{56}{139},-\frac{72}{139}\right]$ is a point on the plane $p$.  The graph shows that the point lies on the plane.

 > $p≔\mathrm{Plane}\left(3x-7y-9z=8\right):$
 > $\mathrm{pt}≔\left[\frac{24}{139},-\frac{56}{139},-\frac{72}{139}\right]:$
 > $\mathrm{Contains}\left(p,\mathrm{pt}\right)$
 ${\mathrm{true}}$ (3)
 > $\mathrm{pp}≔\mathrm{GetPlot}\left(\mathrm{Plane}\left(3x-7y-9z=8\right),\mathrm{caption}="",\mathrm{shownormal}=\mathrm{false},\mathrm{showpoint}=\mathrm{false}\right):$
 > $\mathrm{pt}≔{\mathrm{plots}}_{\mathrm{pointplot3d}}\left(\left[\mathrm{pt}\right],'\mathrm{symbol}'='\mathrm{solidcircle}','\mathrm{symbolsize}'=20,'\mathrm{color}'="black"\right):$
 > ${\mathrm{plots}}_{\mathrm{display}}\left(\left[\mathrm{pp},\mathrm{pt}\right]\right)$

Compatibility

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