← 上一题 返回专题 下一题 → 已知 O O O P 1 ( cos α , sin α ) {P}_{1}\left( {\cos \alpha ,\sin \alpha }\right) P 1 ( cos α , sin α ) P 2 ( cos β , − sin β ) {P}_{2}\left( {\cos \beta , - \sin \beta }\right) P 2 ( cos β , − sin β ) P 3 ( cos ( α + β ) , sin ( α + β ) ) {P}_{3}\left( {\cos \left( {\alpha + \beta }\right) ,\sin \left( {\alpha + \beta }\right) }\right) P 3 ( cos ( α + β ) , sin ( α + β ) ) A ( 1 , 0 ) A\left( {1,0}\right) A ( 1 , 0 ) ∣ O P 1 → ∣ = ∣ O P 2 → ∣ \left| \overrightarrow{O{P}_{1}}\right| = \left| \overrightarrow{O{P}_{2}}\right| O P 1 = O P 2 ∣ A P 1 → ∣ = ∣ A P 2 → ∣ \left| \overrightarrow{A{P}_{1}}\right| = \left| \overrightarrow{A{P}_{2}}\right| A P 1 = A P 2 O A → ⋅ O P 3 → = O P 1 → ⋅ O P 2 → \overrightarrow{OA} \cdot \overrightarrow{O{P}_{3}} = \overrightarrow{O{P}_{1}} \cdot \overrightarrow{O{P}_{2}} O A ⋅ O P 3 = O P 1 ⋅ O P 2 O A → ⋅ O P 1 → = O P 2 → ⋅ O P 3 → \overrightarrow{OA} \cdot \overrightarrow{O{P}_{1}} = \overrightarrow{O{P}_{2}} \cdot \overrightarrow{O{P}_{3}} O A ⋅ O P 1 = O P 2 ⋅ O P 3
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