Question

If |A X B|=(3)^1/2 A.B, then the value of |A+B| is

Answer 1

First of all the question should be

|a×b|=√3a.b because a vector can never be equal to a scalar.

So |a×b|=ab sintheta where theta is angle between 2 vectors.

a.b=ab costheta

Equating above two we get

Sintheta=√3costheta

=> tantheta =√3

=> theta =60 ° or 240° or more general theta = nπ+60°.

so |a+b| =√|a|^2+|b|^2+2|a||b| costheta)

Since we have two different values of theta there are two different answers.

1st answer is√|a|^2+|b|^2+|a||b| )

2nd answer is√|a|^2+|b|^2-|a||b| )