Question

If `|A+B| / |A-B|=1` what is the value of A.B and A X B??

Here both A and B are vectors and A.B denotes dot product and A X B denotes cross product of the vectors A and B.

Answer 1

See below

Explanation:

`|bb A+ bb B| = |bbA - bbB| implies bbA bot bb B, qquad bbA,bbB ne bb0`

So `bbA * bb B= 0`

You can brute force that as:

`(bb A+ bb B) * (bb A+ bb B) = (bb A - bbB ) * (bb A - bb B)`

`A^2 +B^2 + 2 bbA * bb B= A^2 + B^2 - 2 bb A * bb B`

`implies bbA * bb B= 0, qquad bbA, bbB ne bb0`

`bbA times bb B = abs bbA abs bbB sin (pi/2) \ bb hat n`

`= abs bbA abs bbB \ bb hat n`

Where `bb hat n` is the unit vector orthogonal to `bbA` and `bbB`