Expert: Paul Klarreich - 6/21/2008

Question
QUESTION: Can u answer this question - "If the difference of two vectors A and B is perpendicular to their sum, determine the relative magnitude of the vectors?"

ANSWER: Questioner:   Anubhav
Category:  Calculus
Private:  No
 
Subject:  vectors
Question:  Can u answer this question - "If the difference of two vectors A and B is perpendicular to their sum, determine the relative magnitude of the vectors?"
...........................
Hi, Anubhav,

You wrote:

If  

(A - B) * (A + B) = 0,

then we have:
A*A - B*B = 0
or

| A |^2 = | B |^2

Does that do it for you?


---------- FOLLOW-UP ----------

QUESTION: This means that magnitude of A is equal to magnitude of B...but does relative magnitude means magnitude in relation to both the vectors or we have to find out their exact value?

Answer
Questioner:   Anubhav
Category:  Calculus
Private:  No
 
Subject:  Vectors
Question:  QUESTION: Can u answer this question - "If the difference of two vectors A and B is perpendicular to their sum, determine the relative magnitude of the vectors?"
...........................
Hi, Anubhav,

You wrote:

If  

(A - B) * (A + B) = 0,

then we have:
A*A - B*B = 0
or

| A |^2 = | B |^2

Does that do it for you?


---------- FOLLOW-UP ----------

QUESTION: This means that magnitude of A is equal to magnitude of B...

>> Right!  And that is the answer -- it is all you can say.  Relative magnitude does not mean 'how big is your cousin?' it means 'how big is one compared to the other?'

but does relative magnitude means magnitude in relation to both the vectors or we have to find out their exact value?

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A little note:  Do you remember your basic high school geometry?  If so, you would reason that:

If A and B are vectors, then A+B is a diagonal of the parallelogram formed by them.  And  A-B is the OTHER diagonal.  Now there was a theorem: If he diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.  So its sides (the vectors) are the same length.

That's it.  You don't need dot product or anything.