Question

Calcular o ângulo entre os vetores u=(4,1,1) e v=(2,-1,2).

Answer 1

$\displaystyle \cos \theta = \frac{u \cdot v}{||u|| \cdot ||v||} \\ \\ \\ \cos \theta = \frac{(4,1,1) \cdot (2,-1,2)}{\sqrt{4^2 + 1^2 + 1^2} \cdot \sqrt{2^2 + (-1)^2 + 2^2}} \\ \\ \\ \cos \theta = \frac{8-1+2}{\sqrt{18} \cdot \sqrt{9}} \\ \\ \\ \cos \theta = \frac{9}{3\sqrt{18}} \\ \\ \\ \cos \theta = \frac{3}{\sqrt{18}} \\ \\ \\ \arccos(\frac{3}{\sqrt{18}}) \\ \\ \\ \boxed{\boxed{45^o}}$