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由向量的数量积公式a·b=|a||b|·cosθ(θ为向量a与b的夹角),易知|a2|·|b|2≥(a·b)2,当且仅当向量a与b共线时等号成立.别看这个不等式来得容易,它的作用却不可小瞧,用它处理某些数学问题比常规方法简单得多.请看下面的例子.
The scalar product of the vector product a·b=|a||b|·cosθ (θ is the angle between the vectors a and b), it is easy to know that |a2|·|b|2≥(a·b)2. The equal sign holds only when the vectors a and b are collinear. It is easy to look at this inequality, but its role can not be underestimated. Using it to deal with certain mathematical problems is much simpler than the conventional method. See the example below.