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geom3d

  

pole

  

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

 

Calling Sequence

Parameters

Description

Examples

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

withgeom3d:

Obtain the coordinates of the poles of the planes 2x+2y3z+7=0, 4x+z3=0, and 5xy+3z8=0 with respect to the sphere x2+y2+z24x+2y2z=0, and show that they are collinear.

planep1,2x+2y3z+7=0,x,y,z,planep2,4x+z3=0,x,y,z,planep3,5xy+3z8=0,x,y,z

p1,p2,p3

(1)

spheres,x2+y2+z24x+2y2z=0,x,y,z:

poleA,p1,s;poleB,p2,s;poleC,p3,s

A

B

C

(2)

AreCollinearA,B,C

true

(3)

See Also

geom3d[polar]

 


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