The file is pretty messed up, but I think I got the question.
Originally Posted by Jenny20
(I changed the condition on k because the problem statement was not correct. k need not be negative.)
where is the angle between the two vectors.
So the problem statement:
which means that = 0 or 180 degrees. Thus the vectors are parallel or antiparallel.
Vectors which are parallel (or antiparallel) are the same vector, up to a rescaling, ie. there exists a scalar k (which just changes the length of the vector) such that . (k is positive if the vectors are parallel and negative if they are antiparallel.)