Question

найдите синус угла между векторами а(1;2) и в(2;1)

Answer 1

$cosalpha=frac{a*b}{|a|*|b|}$

 

$cosalpha=frac{1*2+2*1}{sqrt{1^{2}+2^{2}}*sqrt{2^{2}+1^{2}}}=frac{4}{sqrt{5}*sqrt{5}}=frac{4}{5}=0,8$

 

$sinalpha=sqrt{1-cos^{2}alpha}=sqrt{1-0,8^{2}}=sqrt{1-0,64}=sqrt{0,36}=0,6$