Stephen wrote:

>> Since you are dealing with lines in 3-space (x,y,z), the lines will only
>> intersect if they lie on the same plane.

> Can that be right?

take two pens, and you will find you can easily hold them
so that they do not intersect, are not parallel, and with the
point of closest approach clearly within the physical pen
boundaries (and not just their projection to infinity).

> What about the lines of the three axis?

any two axes lie within a plane and intersect at the origin.

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