Question

помогите..................

Answer 1

(AB) = (3-4; -1-2; 6-4) = (-1; -3; 2); AC = (2-4; 1-2; 0-4) = (-2; -1; -4)
Угол между AB и AC
$cos(AB;AC)= frac{X1*X2+Y1*Y2+Z1*Z2}{ sqrt{X1^2+Y1^2+Z1^2}*sqrt{X2^2+Y2^2+Z2^2} } =$
$= frac{(-1)(-2)+(-3)(-1)+2(-4)}{ sqrt{(-1)^2+(-3)^2+2^2}* sqrt{(-2)^2+(-1)^2+(-4)^2} } = frac{2+3-8}{ sqrt{1+9+4}* sqrt{4+1+16} } =$
$=frac{-3}{ sqrt{14}* sqrt{21} } = frac{-3}{ sqrt{2}* sqrt{7}* sqrt{3}* sqrt{7}}=- frac{3}{7 sqrt{6} } = - frac{3 sqrt{6} }{7*6}=- frac{ sqrt{6} }{14}$
Угол (AB; AC) = pi - arccos(√6/14)