Let **v** = (3, 4)^{T}

**v · v**= ?- ( 3, 4 )
^{T}**·**( 3, 4 )^{T}= 3^{2}+ 4^{2}= 9 + 16 = 25 =**5**^{2}

- ( 3, 4 )
- The length of
**v**= ? - The length of the vector is
**5**.

Hmm... there might be a connection here....

As you have seen in the previous chapter:

(x, y, z)^{T}·(x, y, z)^{T}= x^{2}+ y^{2}+ z^{2}

Another way of writing this is:

v · v= |v|^{2}

The dot product of a column matrix with itself is a scalar, the square of the length of the vector it represents.

WARNING! When your graphics text starts using *homogeneous coordinates* this
calculation will need to be modified somewhat.
Remember, length is a property of the geometric vector, not an
inherent property of the column matrix that might be used to represent it.