go to previous page   go to home page   go to next page


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

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.


Thought questions: