- 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
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?