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    Vector analysis

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    In R^n with the standard inner product, consider the vector...
    u= (1, 1, 1, ...,1) and the coordinate vectors e_1=(1,0,0,...,0), e_2=(0,1,0,...,0),...,e_n=(0,0,0,...,1)

    a) Compute the angle(s) between u and e_i (in degrees) for dimensions n=2,3
    b) Check that in R^n, <u, e_i>=1 for i=1,2,...,n
    c) Check that even though <u,e_i>=1, the angle theta_i between u and e_i tends to pi/2 as n goes to infinity

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    Solution Preview

    (a) We consider .
    Then the angle between and is .
    The angle ...

    Solution Summary

    Vector analysis is achieved.