Question

How do you find the angle between the vectors `u=cos(pi/4)i+sin(pi/4)j` and `v=cos(pi/2)i+sin(pi/2)j`?

Answer 1

`pi/4` and `7/4pi` (for measurement in the opposite sense)..

Explanation:

`u=1/sqrt 2 i + 1/sqrt 2 j and v=j` are unit (modulus = 1) vectors. The angle in between is

arc cos `(u.v )/(|u||v|)`

`=arc cos^(-1)((1/sqrt 2)(0)+(1/sqrt 2)(1))`

`=arc cos(1/sqrt2)`

`=pi/4`

If the sense of measurement is opposite, this is `2pi-pi/4=7pi/4`