The push or pull that is exerted to an item causes the body to accelerate. The force, as we all know, is a vector. As a consequence, we’ll employ the resulting vector quantities approach. As a consequence, the product of the two vectors A and B is
R = √ A2 + B2 + 2ABcosθ
Here, θ is the angle between the vectors A and B .
Now, it is given in the question that, there are two forces each of magnitude F and their resultant is also of magnitude F .
Therefore, we will put F in place of A , B and R .
Therefore, the resultant F of the two vectors forces each of magnitude F is given by F = √F2 + F2 + 2F.Fcosθ
⇒ F=√2F2 + 2F2cosθ
⇒ F = √2F2(1+cosθ) Now, squaring both the sides,
we get F2 = 2F2(1+cosθ)
⇒ F2/2F2 = 1 + cosθ
⇒ 1/2 = 1 + cosθ
⇒ −1/2 = cosθ
∴ θ = 120∘
Therefore, the angle between the two forces is 120∘ .