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