# 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?

Aug 10, 2016

$\frac{\pi}{4}$ and $\frac{7}{4} \pi$ (for measurement in the opposite sense)..

#### Explanation:

$u = \frac{1}{\sqrt{2}} i + \frac{1}{\sqrt{2}} j \mathmr{and} v = j$ are unit (modulus = 1) vectors. The angle in between is

arc cos $\frac{u . v}{| u | | v |}$

$= a r c {\cos}^{- 1} \left(\left(\frac{1}{\sqrt{2}}\right) \left(0\right) + \left(\frac{1}{\sqrt{2}}\right) \left(1\right)\right)$

$= a r c \cos \left(\frac{1}{\sqrt{2}}\right)$

$= \frac{\pi}{4}$

If the sense of measurement is opposite, this is $2 \pi - \frac{\pi}{4} = 7 \frac{\pi}{4}$