1. Mathematics
2. Geometry and Topology
3. Analytic Geometry
4. Vector Calculus
5. 432751

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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