Question

If|A|=|B| what is the angle between A+B and A-B?

Answer 1

`pi/2`

Explanation:

The angle follows from the definition of the scalar product:

`alpha =cos^(-1)( ((mathbf (A + mathbf B)) * ( mathbf A - mathbf B))/( | mathbf A + mathbf B | | mathbf A - mathbf B| ))`

`= cos^(-1) ((A^2 - mathbf A * mathbf B + mathbf B * mathbf A - B^2)/( | mathbf A + mathbf B | | mathbf A - mathbf B| ))`

`mathbf A * mathbf B` commutes and `A^2 = B^2` so the numerator is zero.

So, provided `mathbf A ne pm mathbf B`:

• `alpha = (n + 1/2) pi`