Question

Two forces, each of magnitude F have a

resultant of the same magnitude F. The

angle between the two forces is

a. 45°

b. 120°

c. 150°

d. 60°​

Answer 1

By the law of parallelogram of vector addition

$r = \sqrt{ {a}^{2} + {b}^{2} + 2ab \cos( \alpha ) }$

substitute the value of r, a and b as F

${f}^{2} = {f}^{2} + {f}^{2} + 2 {f}^{2} \cos( \alpha )$

$- { {f}^{2} = 2 {f}^{2} } \cos( \alpha )$

cos( alpha)= -1/2

alpha=cos^-1(-1/2)

$\alpha = 120 \: degree$

Hope it helps you.