Question

sendo os vetores u=(-1,2) e v=(2,1). o ângulo entre esses dois vetores,em graus,é?

Answer 1

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

temos:
$\Bmatrix{U=(-1,2)\\\\|U|= \sqrt{(-1)^2+2^2} = \sqrt{5} \\\\\\V=(2,1)\\\\|V|= \sqrt{2^2+1^2}= \sqrt{5} \end$

então
$cos(\theta)= \frac{(-1,2)*(2,1)}{ \sqrt{5}* \sqrt{5} } \\\\cos(\theta)= \frac{(-1*2)+(2*1)}{5} \\\\cos(\theta)= \frac{0}{5}\\\\cos(\theta)=0\\\\\theta=arcos(0)\\\\\theta=90^\circ$