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geom3d[ArePerpendicular] - test if two objects are perpendicular to each other
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Calling Sequence
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ArePerpendicular(dseg1, dseg2, cond)
ArePerpendicular(l1, l2, cond)
ArePerpendicular(l1, p1, cond)
ArePerpendicular(p1, p2, cond)
ArePerpendicular(s1, s2, cond)
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Parameters
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dseg1, dseg2
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directed line segments
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l1, l2
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lines
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p1, p2
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planes
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s1, s2
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spheres
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cond
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(optional) name
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Description
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The routine returns true if the given objects are perpendicular to each other; false if they are not; and FAIL if it is unable to reach a conclusion.
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In case of FAIL, if the third optional argument is given, the condition that makes the given objects perpendicular to each other is assigned to this argument.
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The command with(geom3d,ArePerpendicular) allows the use of the abbreviated form of this command.
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Examples
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Show that the following spheres are mutually orthogonal:
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![sphere(s1, x^2+y^2+z^2 = a^2, [x, y, z])](/support/helpjp/helpview.aspx?si=5926/file03971/math141.png)
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![sphere(s2, x^2+y^2+z^2-2*a*y-2*a*z+a^2 = 0, [x, y, z])](/support/helpjp/helpview.aspx?si=5926/file03971/math145.png)
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![sphere(s3, x^2+y^2+z^2-2*a*x-2*a*z+a^2 = 0, [x, y, z])](/support/helpjp/helpview.aspx?si=5926/file03971/math149.png)
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![sphere(s4, x^2+y^2+z^2-2*a*x-2*a*y+a^2 = 0, [x, y, z])](/support/helpjp/helpview.aspx?si=5926/file03971/math153.png)
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| (1) |
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