Question

Найти косинус угла между векторами а(3;5;-1) и b(1;1;4)

Answer 1

$\(\ \overline{a}=\left(a_{x} ; a_{y}\right), \overline{b}=\left(b_{x} ; b_{y}\right)\)\\\\cos(\ \overline{a};\ \overline{b})=\frac{a_x*b_x+a_y*b_y}{\sqrt{a_x^2+a_y^2}*\sqrt{b_x^2+b_y^2}}\\\\\\cos(\ \overline{a};\ \overline{b})=\frac{3*1+5*1+(-1)*4}{\sqrt{3^2+5^2+(-1)^2}*\sqrt{1^2+1^2+4^2}}=\frac{3+5-4}{\sqrt{9+25+1}*\sqrt{1+1+16}}=\\\\=\frac{4}{\sqrt{35}*\sqrt{18}}=\frac{4}{3\sqrt{70}}=\frac{4\sqrt{70}}{3*70}=\frac{2\sqrt{70}}{105}$