Look, similar to the rule you already stated:

taking two vectors, for them to be collinear there must exist one k != 0 such that for all coordinate d: d1 = k * d2

Obviously d1 == 0 iff d2 == 0 because k != 0 !!!

But if one coordinate is 0 for both it doesn't matter which k is chosen for the other ones.

Isn't it obvious now?

You check all coordinates in a loop and break if

Edit
FWIW: There is one edge case left, the zero vector. But a normal vector with all coordinates being 0 looks like a bug to me and should raise an exception.

Cheers Rolf
(addicted to the Perl Programming Language :)
see Wikisyntax for the Monastery

In reply to Re^3: The intersection of M hyperplanes (Ndim) by LanX
in thread The intersection of M hyperplanes (Ndim) by bliako

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