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

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

The length of **v** = 5 since it is part of a 3/4/5 right triangle.

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.

What is the length of the vector represented by ( 2, 1, -1)^{T} ?