(30, 40)^{T} = 10(3, 4)^{T}, so the length is 10*5 = 50

Or, if you want to do it the hard way:

|(30,40)|^{2} = 900 + 1600 = 2500.
The length = 2500 = 50.

Recall that a **unit vector** is a vector of length one.
Creating a unit vector in the same direction as a given vector is
called **normalizing** the vector.
Here is the formula for normalizing a vector (copied from a previous chapter):

v=_{u}v/|v|

The formula works when column matrices are used to represent the vector.
The length **| v |** is frequently calculated by
using the column matrix dot product.

**Potential Confusion:** The word "normal" has several meanings.
Normalizing a vector means making a unit vector in the same direction as the original.
A vector that is perpendicular to a particular surface is sometimes called a
"normal vector"
but is not necessarily a unit vector.
Be careful never to say "normal vector" when you mean "unit vector."