Length is Zero or Positive

Since the square of length is a sum of squares, and squares (of real numbers) are zero or positive, length must always be zero or positive.

|a|  =  | (a1, a2,  a3 )T |

     =  √( a12 + a22 + a32 )
     
    >= 0

The only time the length of a 3D vector is zero is when the vector is the zero vector. In all coordinate frames the 3D zero vector is represented by:

0 =  (0, 0, 0)T

So its length is:

|0|  =  √( 02 + 02 +  02 ) =   0

Of course, the length of the 2D zero vector is also zero, and it is the only 2D vector with zero length.