设向量a,b,c满足a+b+c=0,(a-b)⊥c,a⊥b,若|a|=1,求|a|^2+|b|^2+|c|^2的值设向量a,b,c满足a+b+c=0,(a-b)⊥c,a⊥b,若|a|=1,求|a|^2+|b|^2+|c|^2的值求这个答案中 为什么=-4c*a也就是(a+b+c)^2-2(a*b+b*c+c*a)=-4c*a的详细计算
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![设向量a,b,c满足a+b+c=0,(a-b)⊥c,a⊥b,若|a|=1,求|a|^2+|b|^2+|c|^2的值设向量a,b,c满足a+b+c=0,(a-b)⊥c,a⊥b,若|a|=1,求|a|^2+|b|^2+|c|^2的值求这个答案中 为什么=-4c*a也就是(a+b+c)^2-2(a*b+b*c+c*a)=-4c*a的详细计算](/uploads/image/z/954656-8-6.jpg?t=%E8%AE%BE%E5%90%91%E9%87%8Fa%2Cb%2Cc%E6%BB%A1%E8%B6%B3a%2Bb%2Bc%3D0%2C%28a-b%29%E2%8A%A5c%2Ca%E2%8A%A5b%2C%E8%8B%A5%7Ca%7C%3D1%2C%E6%B1%82%7Ca%7C%5E2%2B%7Cb%7C%5E2%2B%7Cc%7C%5E2%E7%9A%84%E5%80%BC%E8%AE%BE%E5%90%91%E9%87%8Fa%2Cb%2Cc%E6%BB%A1%E8%B6%B3a%2Bb%2Bc%3D0%2C%28a-b%29%E2%8A%A5c%2Ca%E2%8A%A5b%2C%E8%8B%A5%7Ca%7C%3D1%2C%E6%B1%82%7Ca%7C%5E2%2B%7Cb%7C%5E2%2B%7Cc%7C%5E2%E7%9A%84%E5%80%BC%E6%B1%82%E8%BF%99%E4%B8%AA%E7%AD%94%E6%A1%88%E4%B8%AD+%E4%B8%BA%E4%BB%80%E4%B9%88%3D-4c%2Aa%E4%B9%9F%E5%B0%B1%E6%98%AF%EF%BC%88a%2Bb%2Bc%29%5E2-2%28a%2Ab%2Bb%2Ac%2Bc%2Aa%29%3D-4c%2Aa%E7%9A%84%E8%AF%A6%E7%BB%86%E8%AE%A1%E7%AE%97)
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