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.

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

$\mathrm{plane}\left(\mathrm{p1}\,2x+2y-3z+7=0\,\left[x\,y\,z\right]\right),\mathrm{plane}\left(\mathrm{p2}\,4x+z-3=0\,\left[x\,y\,z\right]\right),\mathrm{plane}\left(\mathrm{p3}\,5x-y+3z-8=0\,\left[x\,y\,z\right]\right)$

$\mathrm{p1},\mathrm{p2},\mathrm{p3}$

$\mathrm{sphere}\left(s\,x^2+y^2+z^2-4x+2y-2z=0\,\left[x\,y\,z\right]\right)\:$

$\mathrm{pole}\left(A\,\mathrm{p1}\,s\right)\;$$\mathrm{pole}\left(B\,\mathrm{p2}\,s\right)\;$$\mathrm{pole}\left(C\,\mathrm{p3}\,s\right)$

$A$

$B$

$C$

$\mathrm{AreCollinear}\left(A\,B\,C\right)$

$\mathrm{true}$