In the coordinate plane, let $O$ be the origin, and let $A$ and $B$ be two distinct points different from $O$. Let $C_{1}$, $C_{2}$, $C_{3}$ be three points in the plane satisfying $\overrightarrow{OC}_{n} = \overrightarrow{OA} + n\overrightarrow{OB}$, $n = 1, 2, 3$. Select the correct options. (1) $\overrightarrow{OC}_{1} \neq \overrightarrow{0}$ (2) $\overline{OC_{1}} < \overline{OC_{2}} < \overline{OC_{3}}$ (3) $\overrightarrow{OC}_{1} \cdot \overrightarrow{OA} < \overrightarrow{OC}_{2} \cdot \overrightarrow{OA} < \overrightarrow{OC}_{3} \cdot \overrightarrow{OA}$ (4) $\overrightarrow{OC_{1}} \cdot \overrightarrow{OB} < \overrightarrow{OC_{2}} \cdot \overrightarrow{OB} < \overrightarrow{OC_{3}} \cdot \overrightarrow{OB}$ (5) $C_{1}$, $C_{2}$, $C_{3}$ are collinear
In the coordinate plane, let $O$ be the origin, and let $A$ and $B$ be two distinct points different from $O$. Let $C_{1}$, $C_{2}$, $C_{3}$ be three points in the plane satisfying $\overrightarrow{OC}_{n} = \overrightarrow{OA} + n\overrightarrow{OB}$, $n = 1, 2, 3$. Select the correct options.\\
(1) $\overrightarrow{OC}_{1} \neq \overrightarrow{0}$\\
(2) $\overline{OC_{1}} < \overline{OC_{2}} < \overline{OC_{3}}$\\
(3) $\overrightarrow{OC}_{1} \cdot \overrightarrow{OA} < \overrightarrow{OC}_{2} \cdot \overrightarrow{OA} < \overrightarrow{OC}_{3} \cdot \overrightarrow{OA}$\\
(4) $\overrightarrow{OC_{1}} \cdot \overrightarrow{OB} < \overrightarrow{OC_{2}} \cdot \overrightarrow{OB} < \overrightarrow{OC_{3}} \cdot \overrightarrow{OB}$\\
(5) $C_{1}$, $C_{2}$, $C_{3}$ are collinear