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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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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.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

Â© BrainMass Inc. brainmass.com December 24, 2021, 10:00 pm ad1c9bdddf>
https://brainmass.com/math/vector-calculus/vector-analysis-432751