Let the $\operatorname { arc } A C$ of a circle subtend a right angle at the centre $O$. If the point $B$ on the arc $A C$, divides the arc $A C$ such that $\frac { \text { length of } \operatorname { arc } A B } { \text { length of } \operatorname { arc } B C } = \frac { 1 } { 5 }$, and $\overrightarrow { O C } = \alpha \overrightarrow { O A } + \beta \overrightarrow { O B }$, then $\alpha + \sqrt { 2 } ( \sqrt { 3 } - 1 ) \beta$ is equal to (1) $2 \sqrt { 3 }$ (2) $2 - \sqrt { 3 }$ (3) $5 \sqrt { 3 }$ (4) $2 + \sqrt { 3 }$
Let the $\operatorname { arc } A C$ of a circle subtend a right angle at the centre $O$. If the point $B$ on the arc $A C$, divides the arc $A C$ such that $\frac { \text { length of } \operatorname { arc } A B } { \text { length of } \operatorname { arc } B C } = \frac { 1 } { 5 }$, and $\overrightarrow { O C } = \alpha \overrightarrow { O A } + \beta \overrightarrow { O B }$, then $\alpha + \sqrt { 2 } ( \sqrt { 3 } - 1 ) \beta$ is equal to\\
(1) $2 \sqrt { 3 }$\\
(2) $2 - \sqrt { 3 }$\\
(3) $5 \sqrt { 3 }$\\
(4) $2 + \sqrt { 3 }$