Two forces of equal magnitude simultaneously act at a point. It is observed that the resultant force is equal in magnitude to the individual forces. Which of the following statements is/are correct? I. The angle between one of the individual forces and the resultant force is /3 . II. The angle between the individual forces is 2 /3 .

Step-by-step solution

Let the two forces be F₁ and F₂ , and their resultant be R . Given that | F₁ | = | F₂ | = | R | = F . The magnitude of the resultant of two vectors is given by R^2 = F₁^2 + F₂^2 + 2F₁ F₂ , where is the angle between the two forces. Substituting the given values: F^2 = F^2 + F^2 + 2F^2 F^2 = 2F^2(1 + ) = - 1 2 = 2 3 Thus, the angle between the individual forces is 2 3 . Statement II is correct. Since the two forces are equal in magnitude, their resultant bisects the angle between them. Let be the angle between the r