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.

1 Answer
Jun 10, 2018

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#