Question

Determine o cosseno dos ângulos entre os vetores: u = (3, 4, 7) e v = (1, 5, 6).

Answer 1

$u=(x_1,y_1,z_1)\ \to\ u=(3,4,7)$

$v=(x_2,y_2,z_2)\ \to\ v=(1,5,6)$

$<u,v>=|u||v|\cos{\phi}\ \to\ \boxed{\cos{\phi}=\dfrac{<u,v>}{|u||v|}}$

$\cos{\phi}=\dfrac{x_1x_2+y_1y_2+z_1z_2}{\sqrt{x_1^2+y_1^2+z_1^2}\sqrt{x_2^2+y_2^2+z_2^2}}$

$\cos{\phi}=\dfrac{(3)(1)+(4)(5)+(7)(6)}{\sqrt{3^2+4^2+7^2}\sqrt{1^2+5^2+6^2}}$

$\cos{\phi}=\dfrac{65}{\sqrt{74}\sqrt{62}}\ \to\ \boxed{\cos{\phi}=\dfrac{65}{2\sqrt{37}\sqrt{31}}}$