Question

Two vectors each of magnitude A have a resultant of same magnitude A. The angle b/w the vectors are?

Answer 1

Two vector A and B make an angle @ then the resultant vector
C={ A^2 + B^2 + 2 AB cos @}^(1/2)
or, C^2= A^2 +B^2 +2AB cos@

here , A= A, B = A and C= A
so,
A^2 = A^2+ A^2 + 2AA cos@
or, -A^2=2A^2 cos @
or, cos@ = -(1/2)
so, @=120° { taking 0°<@<180°}

Answer 2

A^2= 2A^2 + 2A^2 cos (theta)
=> theta= cos inverse (-1/2)
=> theta = 120° or 240°