已知 $\overset{\large\rightharpoonup}{OC_n} = \overset{\large\rightharpoonup}{OA} + n \overset{\large\rightharpoonup}{OB}$，$n=1,2,3$。 (1) 錯誤。若 $\overset{\large\rightharpoonup}{OA} = -\overset{\large\rightharpoonup}{OB}$，則 $\overset{\large\rightharpoonup}{OC_1} = \mathbf{0}$。 (2) 錯誤。$|\overset{\large\rightharpoonup}{OC_n}|^2 = |\overset{\large\rightharpoonup}{OA}|^2 + n^2 |\overset{\large\rightharpoonup}{OB}|^2 + 2n \overset{\large\rightharpoonup}{OA} \cdot \overset{\large\rightharpoonup}{OB}$，其增減性質取決於 $\overset{\large\rightharpoonup}{OA} \cdot \overset{\large\rightharpoonup}{OB}$。若內積為負且絕對值較大，則不一定遞增。 (3) 錯誤。$\overset{\large\rightharpoonup}{OC_n} \cdot \overset{\large\rightharpoonup}{OA} = |\overset{\large\rightharpoonup}{OA}|^2 + n \overset{\large\rightharpoonup}{OB} \cdot \overset{\large\rightharpoonup}{OA}$，其增減性取決於 $\overset{\large\rightharpoonup}{OA} \cdot \overset{\large\rightharpoonup}{OB}$ 的正負。 (4) 正確。$\overset{\large\rightharpoonup}{OC_n} \cdot \overset{\large\rightharpoonup}{OB} = \overset{\large\rightharpoonup}{OA} \cdot \overset{\large\rightharpoonup}{OB} + n |\overset{\large\rightharpoonup}{OB}|^2$。因 $B \neq O$，故 $|\overset{\large\rightharpoonup}{OB}|^2 > 0$，此式隨 $n$ 增大而遞增。 (5) 正確。$\overset{\large\rightharpoonup}{C_1C_2} = \overset{\large\rightharpoonup}{OC_2} - \overset{\large\rightharpoonup}{OC_1} = \overset{\large\rightharpoonup}{OB}$，$\overset{\large\rightharpoonup}{C_2C_3} = \overset{\large\rightharpoonup}{OC_3} - \overset{\large\rightharpoonup}{OC_2} = \overset{\large\rightharpoonup}{OB}$。因向量相同且共用點 $C_2$，故三點共線。 故選 (4)(5)。