좌표평면에서 세 점 A ( − 3 , 1 ) , B ( 0 , 2 ) , C ( 1 , 0 ) \mathrm{A}\left(-3,\,1\right),\,\mathrm{B}\left(0,\,2\right),\,\mathrm{C}\left(1,\,0\right) A ( − 3 , 1 ) , B ( 0 , 2 ) , C ( 1 , 0 ) P , Q \mathrm{P},\,\mathrm{Q} P , Q
∣ A P → ∣ = 1 , ∣ B Q → ∣ = 2 , A P → ⋅ O C → ≥ 2 2 \left|\overrightarrow{\mathrm{AP}}\right|=1,\,\quad \left|\overrightarrow{\mathrm{BQ}}\right|=2,\,\quad \overrightarrow{\mathrm{AP}}\cdot\overrightarrow{\mathrm{OC}}\ge\dfrac{\sqrt2}{2} AP = 1 , BQ = 2 , AP ⋅ OC ≥ 2 2 를 만족시킬 때, A P → ⋅ A Q → \overrightarrow{\mathrm{AP}}\cdot\overrightarrow{\mathrm{AQ}} AP ⋅ AQ P , Q \mathrm{P},\,\mathrm{Q} P , Q P 0 , Q 0 \mathrm{P}_0,\,\mathrm{Q}_0 P 0 , Q 0 A P 0 \mathrm{AP}_0 AP 0 X \mathrm{X} X B X → ⋅ B Q 0 → ≥ 1 \overrightarrow{\mathrm{BX}}\cdot\overrightarrow{\mathrm{BQ}_0}\ge1 BX ⋅ BQ 0 ≥ 1 ∣ Q 0 X → ∣ 2 \left|\overrightarrow{\mathrm{Q}_0\mathrm{X}}\right|^2 Q 0 X 2 q p \dfrac{q}{p} p q p + q p+q p + q O \mathrm{O} O p p p q q q
