Question

Considere os vetores u=(2,-1,1) e v=(1,1,2). Encontre u.v e determine o ângulo 'teta" entre eles.

Answer 1

$\boxed{\boxed{cos(\theta)= \frac{U*V}{||U||*||V||} }}$

$\text{temos:}\\\\\Bmatrix{U=(2,-1,1)\\\\||U||= \sqrt{2^2+(-1)~2+1^2} = \sqrt{6}\\\\\\\\V=(1,1,2)\\\\\||V||= \sqrt{1^2+1^2+2^2}= \sqrt{6} \end$

calculando o angulo

$cos(\theta)= \frac{(2,-1,1)*(1,1,2)}{\sqrt{6}*\sqrt{6}} \\\\cos(\theta)= \frac{(2*1)+(-1*1)+(1*2)}{(\sqrt{6})^2}\\\\cos(\theta)= \frac{3}{6}= \frac{1}{2} \\\\\\\ \boxed{\theta=arcos\left( \frac{1}{2}\right)=60^\circ }$