Question

evaluating if two vectors are parallel to each other.

Answer 1

If they are then one is a scalar multiple of the other. So you can divide each entry by its vectors magnitude. Do this for each vector and if they are the same afterwards, then they are parallel.

Or just look and see if one is a multiple of the other.

Answer 2

Also, \(\vec{u}\times \vec{v}=\vec{0}\), where \(\times\) is the cross product, then they are parallel.

Answer 3

An interesting idea is that the zero vector is parallel to every vector. Another interesting fact is you can produce the zero vector by combining two vectors only when the vectors are parallel.

Answer 4

Two non-zero vectors \(u\) and \(v\) are parallel if there is some scalar \(c\) such that \(u = cv\)