Question

Determinar, aproximadamente, o ângulo entre os pares de vetores: a) u =(2,1) e v =(4,-2)

Answer 1

$\arccos \theta = \displaystyle \frac{u \cdot v}{||u|| \cdot ||v||} \\ \\ \\ \arccos \theta =\displaystyle \frac{(2,1) \cdot (4,-2)}{ \sqrt{2^{2}+1^{2}} \cdot \sqrt{4^{2}+(-2)^{2}} } \\ \\ \\ \arccos \theta =\displaystyle \frac{6}{ \sqrt{5} \cdot \sqrt{20} } \\ \\ \\ \arccos \theta =\displaystyle \frac{6}{ \sqrt{100} } \\ \\ \\ \arccos \theta =\displaystyle \frac{6}{10} \\ \\ \\ \arccos \theta =\displaystyle \frac{3}{5} \to \boxed{\boxed{53,13^{o}}}$