To solve this problem, we need to analyze the scenario where two forces of equal magnitude act on a point and create a resultant force equal in magnitude to each of the individual forces.

Let the magnitude of each force be \(F\). Using vector addition, the resultant force, \(R\), due to two forces making an angle \(\theta\) with each other is given by the formula:

\(R = \sqrt{F^2 + F^2 + 2F \cdot F \cdot \cos(\theta)}\)

Since the resultant force is equal to the magnitude of each individual force, we have:

\(F = \sqrt{F^2 + F^2 + 2F \cdot F \cdot \cos(\theta)}\)

Simplifying, we get:

• \(F^2 = 2F^2(1 + \cos(\theta))\)
• \(1 = 2(1 + \cos(\theta))\)
• \(1 = 2 + 2\cos(\theta)\)
• \(2\cos(\theta) = -1\)
• \(\cos(\theta) = -\frac{1}{2}\)
• This yields \(\theta = \frac{2\pi}{3}\) (or 120 degrees)

Thus, statement II is correct: The angle between the individual forces is \(\frac{2\pi}{3}\).

Next, to find the angle between one of the individual forces and the resultant, note that for a parallelogram consisting of two adjacent equal forces and one diagonal (resultant), each of the two equal adjacent sides angles with this diagonal by half of the total angle between them:

If \(\theta = \frac{2\pi}{3} = 120^\circ\), then each angle above is \(\frac{\pi}{3} = 60^\circ\).

Thus, statement I is also correct: The angle between one of the individual forces and the resultant force is \(\pi/3\).

Therefore, the correct answer is: Both I and II