Let a, b, and c be vectors of equal magnitude such that the angle between a and b is α, between b and c is β, and between c and a is γ. Then the minimum value of cos(α) + cos(β) + cos(γ) is:

Two forces vector A and vector B have magnitudes A and B respectively, and their resultant vector R has magnitude R. If force B is doubled, then magnitude R is doubled. Similarly, if force B is reversed, then magnitude R is also doubled. What is the ratio A : B : R?