Will two vectors that are equal to each other have the same length?
- -- YES, since corresponding elements must be equal, so corresponding squares must be equal, so the sum must be equal, so the length must be equal.
Will two vectors that have the same length always be equal to each other?
- -- NO. It is possible for the sum of the squared elements to be equal without the elements themselves being equal.

Length of the Negative of a Vector

If v is a vector, then -v is a vector pointing in the opposite direction.

If v is represented by (a, b, c)^T then -v is represented by (-a, -b, -c)^T.

What is the relation between the length of v and the length of -v?