If the resultant of two equal forces is root2 times a single force find the angle between them?

If two equal forces ( F ) are acting at an angle ( \theta ), the resultant ( R ) can be calculated using the formula ( R = F \sqrt{2(1 + \cos\theta)} ). Given that the resultant is ( \sqrt{2} F ), we can set up the equation ( \sqrt{2} F = F \sqrt{2(1 + \cos\theta)} ). Dividing through by ( F ) (assuming ( F \neq 0 )), we have ( \sqrt{2} = \sqrt{2(1 + \cos\theta)} ). Squaring both sides gives ( 2 = 2(1 + \cos\theta) ), which simplifies to ( \cos\theta = 0 ). Therefore, the angle ( \theta ) between the two forces is ( 90^\circ ).