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geom3d[distance] - find the distance between two given objects
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Calling Sequence
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distance(A, B)
distance(l1, l2)
distance(p1, p2)
distance(A, l1)
distance(A, p1)
distance(l1, p1)
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Parameters
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A, B
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points
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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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Description
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The routine computes the distance between two given objects: points, lines, and planes, or any combination of these.
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The command with(geom3d,distance) allows the use of the abbreviated form of this command.
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Examples
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Distance from a point to a plane
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![plane(pp, l*x+m*y+n*z+p = 0, [x, y, z])](/support/helpjp/helpview.aspx?si=4869/file04002/math107.png)
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![point(A, [x1, y1, z1])](/support/helpjp/helpview.aspx?si=4869/file04002/math111.png)
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Find the distance from a point to a straight line
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![point(A, 6, 6, -1), line(l, [2+t, 1+2*t, -3-t], t)](/support/helpjp/helpview.aspx?si=4869/file04002/math128.png)
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Find the two points on the line x=2*y=3*z+6 at a distance of 7 units from the plane 2*x+y-2*z=5.
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![plane(p, 2*x+y-2*z = 5, [x, y, z])](/support/helpjp/helpview.aspx?si=4869/file04002/math145.png)
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![ans := [solve(d = 7, t)]](/support/helpjp/helpview.aspx?si=4869/file04002/math153.png)
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coordinates of the two points are
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![[[12, 6, 2], [-120/11, -60/11, -62/11]]](/support/helpjp/helpview.aspx?si=4869/file04002/math166.png)
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