Question

Calcular o ângulo entre os valores =(2,2,4) e =(-1,3,3)

Answer 1

$cos \alpha = \frac{(2.2.4) \times ( - 1.3.3)}{ \sqrt{2 {}^{2} + 2 {}^{2} + 4 {}^{2} } \times \sqrt{ {( - 1)}^{2} + {3}^{2} + {3}^{2} } } = \frac{2 \times ( - 1) + 2 \times 3 + 4 \times 3}{ \sqrt{24} \times \sqrt{19} } = \frac{ - 2 + 6 + 12}{ \sqrt{456} } = \frac{16}{ \sqrt{ {2}^{3} \times 57} } = \frac{16}{2 \sqrt{114} } = \frac{8}{ \sqrt{114} } = \frac{8 \sqrt{114} }{114} = \frac{4 \sqrt{114} }{57}$

$\frac{4 \sqrt{114} }{57} = 0.7492686493 \\ \\ arc \: cos =~ 42 \: graus$