More Practice

It would be good to practice that idea. The diagram shows a vector and two coordinate frames; a light gray frame and an orange frame.

In the light gray frame the vector is represented by (8, 6)^T. In the orange frame the vector is represented by (9.8, 2)^T. Say that the axes of both frames are calibrated using the same units (inches, for example).

Using the first representation the length of the vector is:

( 82 + 62 ) 
  =   ( 64 + 36 )
  =   ( 100 )
  =   10.0

Using the second representation the length of the vector is:

( 9.82 + 22 ) 
  =   ( 96 + 4 )
  =   ( 100 )
  =   10.0