Yes. Vectors don't have position, so in pictures the tail can be placed anywhere.

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|= | (a_{1}, a_{2}, a_{3})^{T}| = √( a_{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.

Thought questions:

- Will two vectors that are equal to each other have the same length?
- Will two vectors that have the same length always be equal to each other?