Checking whether two lines or two spheres in space are orthogonal

### 25.11.5 Checking whether two lines or two spheres in space are orthogonal

See Section 24.15.13 for checking for orthogonality in two-dimensional geometry.

The is_orthogonal command determines whether or not two objects are orthogonal.

- is_orthogonal takes two arguments: L,P, which can be two lines, two spheres, two planes or a line and a plane.
- is_orthogonal(L,P) returns 1 is the objects are orthogonal; it returns 0 otherwise.

#### Examples

is_orthogonal(line([2,3,-2],[-1,-1,-1]),line([1,0,0],[1,2,8]))

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is_orthogonal(line([2,3,-2],[-1,-1,-1]),plane([-1,-1,-1],[-1,0,3],[-2,0,0]))

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is_orthogonal(plane([0,0,0],[1,2,-3],[1,1,-2]),plane([-1,-1,-1],[1,2,-3],[0,0,0]))

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is_orthogonal(sphere([0,0,0],sqrt(2)),sphere([2,0,0],sqrt(2)))

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