A student works three problems involving the addition of two different vectors, \(\overrightarrow{\mathbf{F}}_{1}\) and \(\overrightarrow{\mathbf{F}}_{2}\). He states that the magnitudes of the three resultants are given by

(a) \(F_{1}+F_{2}\),

(b) \(F_{1}-F_{2}\), and

(c) \(\sqrt{F_{1}^{2}+F_{2}^{2}}\). Are these results possible? If so, describe the vectors in each case.