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

**| v |** = **| -v |**

You can see this mechanically:

| v | = |(a, b, c)^{T}| = ( a^{2}+ b^{2}+ c^{2}) |-v | = |(-a, -b, -c)^{T}| = ( -a^{2}+ -b^{2}+ -c^{2}) = ( a^{2}+ b^{2}+ c^{2})

The diagram shows this graphically (in two dimensions).

You would like to say that the two vectors are the same length,
but point in opposite directions.
In fact, you *can* say that.
The next chapter will give you the authority to do so.