# 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

https://brainmass.com/math/vector-calculus/vector-analysis-432751

## SOLUTION This solution is **FREE** courtesy of BrainMass!

(a) We consider .

Then the angle between and is .

The angle between and is .

We consider

Then the angle between and is .

Then we have ,

(b) Now for general , the angle between and is .

Then we have ,

(c) Since , when , we have . Done.

https://brainmass.com/math/vector-calculus/vector-analysis-432751