Assignment:
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, =1 for i=1,2,...,n
c) Check that even though =1, the angle theta_i between u and e_i tends to pi/2 as n goes to infinity.
Provide complete and step by step solution for the question and show calculations and use formulas.