Question

At what angle the two forces of magnitude A+B and A-B act so that resultant is √3A²+B²
??????

Answer 1

Explanation:

We have two vectors those being,

A+B

A−B

Their sum is 2A . I assume what we want is that this equals 3|A|2+|B|2−−−−−−−−−−√ in magnitude. This implies that,

4|A|2=3|A|2+|B|2

With some rearangment, in the language of dot products, this means that,

(A−B)⋅(A+B)=0

Hence the vectors are orthogonal. Furthermore it is easy to see that the vectors A,B should be equal in magnitude.