Question

Вычислите косинус угла между векторами а=(3;1;2) и b=(1; 1,5; 0,5)

Answer 1

$|a|=sqrt{3^2+1^2+2^2}=sqrt{9+1+4}=sqrt{14};\ |b|=sqrt{1^2+1.5^2+0.5^2}=sqrt{1+2.25+0.25}=sqrt{3.5};\ ab=3*1+1*1.5+2*0.5=3+1.5+1=5.5;\ cos (a, b)=frac{ab}{|a||b|}=frac{5.5}{sqrt{14}*sqrt{3.5}}=frac{5.5}{sqrt{14*3.5}}=frac{5.5}{sqrt{49}}=frac{5.5}{7}=frac{55}{70}=frac{11}{14}$