已知平面向量A=（cosa,sina),B=(cosb,sinb),|A-B|=2根号5/5

学习时间:2026-04-07 19:43:07 阅读：864

已知平面向量A=（cosa,sina),B=(cosb,sinb),|A-B|=2根号5/5（1）求cos(a-b)的值（2）0＜a＜π/2,-π/2＜b＜0,且sinb=-5/13,求sina的值

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2026-04-07 19:43:07

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A-B=(cosa-cosb, sina-sinb)|A-B|^2=(cosa-cosb)^2+(sina-sinb)^2=2-2(cosacosb+sinasinb)=4/5cosacosb+sinasinb=3/5cos(a-b)=cosacosb+sinasinb=3/5-π/2