Question

Calcular o angulo entre os vetores u= ( (\sqrt{3} ,2) ) e v=(1,0) ?

Answer 1

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

temos
$U= (\sqrt{3} ,2)\\\\|U|= \sqrt{( \sqrt{3} )^2+(2)^2} = \sqrt{7}\\\\\\\\V=(1,0)\\\\|V|= \sqrt{(1)^2+(0)^2} =1$

então

$cos(\theta) = \frac{( \sqrt{3},2).(1,0) }{ \sqrt{7}*1 } \\\\cos(\theta)= \frac{( \sqrt{3}*1)+(2*0) }{ \sqrt{7} } \\\\cos(\theta)= \frac{\sqrt{3}}{\sqrt{7}} \\\\\theta=arcos \left( \frac{\sqrt{3}}{\sqrt{7}} \right)\approx 49,11^\circ$