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    Inequality: Proof using Unit Vectors

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    Prove that (a1b1+a2b2+...+anbn)^2<=(a1^2+a2^2+...+an^2)(b1^2+b2^2+...+bn^2)
    where ai, bi are real numbers, i=1,2,...,n

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    Solution Preview

    Proof. Consider two vectors x=(a1,a2,...,an) and y=(b1,b2,...,bn). If all ai's are equal zero or all bi's are equal zero, then x=(0,0,...,0) ...

    Solution Summary

    An inequality is proven using unit vectors. Function vectors are examined.