Question

resultant of 2 vectors A and B of the same magnitude and inclined at an angle theta has a magnitude equal to either of them. find theta

Answer 1

Dear student,

The resultant (R) of two forces (A and B) is mathematically represented as

R² = A² + B² + 2ABCosθ

where θ is the angle between forces A and B. Now, as all three forces are equal, so

let R = A = B = x

So,

x² = x² + x² + 2x.xCosθ

or x² = 2x² (1 + Cosθ)

1/2 = 1 + Cosθ

thus , Cosθ = -1/2

or θ = 120 ^o
Regards