pole - Maple Help

geom3d

 pole
 find the pole of a given plane with respect to a given sphere

 Calling Sequence pole(A, p, s)

Parameters

 A - the name of the pole p - plane s - sphere

Description

 • The pole of a plane p with respect to a sphere is defined to be the point whose polar is the given plane p.
 • For a detailed description of the pole of A, use the routine detail.
 • The command with(geom3d,pole) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{geom3d}\right):$

Obtain the coordinates of the poles of the planes $2x+2y-3z+7=0$, $4x+z-3=0$, and $5x-y+3z-8=0$ with respect to the sphere ${x}^{2}+{y}^{2}+{z}^{2}-4x+2y-2z=0$, and show that they are collinear.

 > $\mathrm{plane}\left(\mathrm{p1},2x+2y-3z+7=0,\left[x,y,z\right]\right),\mathrm{plane}\left(\mathrm{p2},4x+z-3=0,\left[x,y,z\right]\right),\mathrm{plane}\left(\mathrm{p3},5x-y+3z-8=0,\left[x,y,z\right]\right)$
 ${\mathrm{p1}}{,}{\mathrm{p2}}{,}{\mathrm{p3}}$ (1)
 > $\mathrm{sphere}\left(s,{x}^{2}+{y}^{2}+{z}^{2}-4x+2y-2z=0,\left[x,y,z\right]\right):$
 > $\mathrm{pole}\left(A,\mathrm{p1},s\right);$$\mathrm{pole}\left(B,\mathrm{p2},s\right);$$\mathrm{pole}\left(C,\mathrm{p3},s\right)$
 ${A}$
 ${B}$
 ${C}$ (2)
 > $\mathrm{AreCollinear}\left(A,B,C\right)$
 ${\mathrm{true}}$ (3)