Question: prove 2 vectors are parallel?
Answer: 2 vectors are parallel if the angle between them is 0 degrees or 180 degrees. At 0 degrees or 180 degrees, the cosine will be 1 or -1 and the cosine squared will be 1. At all other angles, the cosine squared will be less than 1. So any 2 vectors are parallel if the above formula is true (equal to zero).