由向量加法可得： $$\overset{\large\rightharpoonup}{AQ} = \overset{\large\rightharpoonup}{AP} + \overset{\large\rightharpoonup}{PQ} = -\overset{\large\rightharpoonup}{PA} + \overset{\large\rightharpoonup}{PQ} = -(4, 3) + (1, 5) = (-3, 2)$$ 因為 $\overline{AQ} = 2\overline{QC}$ 且 $Q$ 在 $AC$ 上，故： $$\overset{\large\rightharpoonup}{AC} = \dfrac{3}{2}\overset{\large\rightharpoonup}{AQ} = \dfrac{3}{2}(-3, 2) = \left(-\dfrac{9}{2}, 3\right)$$ 又 $P$ 是 $BC$ 的中點，故： $$\overset{\large\rightharpoonup}{PC} = \overset{\large\rightharpoonup}{PA} + \overset{\large\rightharpoonup}{AC} = (4, 3) + \left(-\dfrac{9}{2}, 3\right) = \left(-\dfrac{1}{2}, 6\right)$$ 因為 $P$ 是 $BC$ 的中點，所以： $$\overset{\large\rightharpoonup}{BC} = 2\overset{\large\rightharpoonup}{PC} = 2\left(-\dfrac{1}{2}, 6\right) = (-1, 12)$$ 故填 $(-1, 12)$。