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For example, let us consider our old friend \(\vec{A} = 5 \hat{i} + 7 \hat{j}\). Clearly, \(A_x = 5, A_y = 7\). The magnitude is thus

\(\sqrt{5^2 + 7^2} = 8.6\)

The angle is

\(\tan^{-1} \left(\frac{A_y}{A_x}\right) = \tan^{-1} \left(\frac{7}{5}\right) = 54^{\circ}\)