A good answer might be:

Let v = (3, 4)T

  1. v · v = ?
    • ( 3, 4 )T · ( 3, 4 )T = 32 + 42 = 9 + 16 = 25 = 52

  2. The length of v = ?

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


Dot Product Formula for Length

As you have seen in the previous chapter:

(x, y, z)T  ·  (x, y, z)T   =   x2 + y2 + z2

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.

QUESTION 2:

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