Hello!
Recently, I found in my textbook that says collinearity is not equivalence relation on the set of all vectors. But I don't agree with this statement. Any two vectors are collinear if and only if they are parallel.
So a || a is true.
a||b => b||a is true.
and finally:
a||b ^ b||c =>a || c
which is again true.
What is the problem?