What is the length of (1,0)^{T} ?

1.0

The vector has a length of one because it is aligned with the x axis (in the current coordinate frame). When represented by a column matrix its only non-zero element is 1.0. Of course, vectors not aligned with any axis also can have a length of one.

A **unit vector** is a vector with a length of one.

Does the following represent a unit vector: (1, 1, 1)^{T} ?