Is the distinction between an object and its representation of any importance in computer science?

A good answer might be:

Yes, it is one of the most important ideas in computer science.


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

QUESTION 10:

If you calculate the length of a vector and get a negative number, what must be true?