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geom3d[pole] - find the pole of a given plane with respect to a given sphere
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Calling Sequence
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pole(A, p, s)
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Parameters
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A
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the name of the pole
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p
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plane
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s
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sphere
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Description
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The pole of a plane p with respect to a sphere is defined to be the point whose polar is the given plane p.
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For a detailed description of the pole of A, use the routine detail.
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The command with(geom3d,pole) allows the use of the abbreviated form of this command.
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Examples
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>
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Obtain the coordinates of the poles of the planes 2*x+2*y-3*z+7=0, 4*x+z-3=0, and 5*x-y+3*z-8=0 with respect to the sphere x^2+y^2+z^2-4*x+2*y-2*z=0, and show that they are collinear.
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![plane(p1, 2*x+2*y-3*z+7 = 0, [x, y, z]), plane(p2, 4*x+z-3 = 0, [x, y, z]), plane(p3, 5*x-y+3*z-8 = 0, [x, y, z])](/support/helpjp/helpview.aspx?si=5942/file04022/math85.png)
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![sphere(s, x^2+y^2+z^2-4*x+2*y-2*z = 0, [x, y, z])](/support/helpjp/helpview.aspx?si=5942/file04022/math92.png)
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