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

| a |=| (a= ( a_{1}, a_{2}, a_{3})^{T}|_{1}^{2}+ a_{2}^{2}+ a_{3}^{2}) >= 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 |= ( 0^{2}+ 0^{2}+ 0^{2}) = 0

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