두 벡터 $\overrightarrow{u} = (1, 2, \sqrt{3}), \overrightarrow{v} = (a, 0, b)$ 가 $\left \| \overrightarrow{u} \times \overrightarrow{v} \right \| = \left \| \overrightarrow{u} \right \| \left \| \overrightarrow{v} \right \|$, $\left \| \overrightarrow{u} + \overrightarrow{v} \right \| ^ {2} = \left \| \overrightarrow{u} \right \| ^ {2} +1$ 을 만족시킬 때, $\displaystyle \frac{b^ {2}} {a^ {2}}$ 의 값은?

• ①$\displaystyle \frac{1} {6}$
• ②$\displaystyle \frac{1} {3}$
• ③$\displaystyle \frac{1} {2}$
• ④$\displaystyle \frac{2} {3}$
• ⑤$\displaystyle \frac{5} {6}$