N((-4)+(-2)/2; (1+(-3))/2; (3+1)/2)=N(-3; -1;2)
vector{AB}=(-2-(-4);-3-1;1-3)=(2;-4;-2)
vector{CN}=(-3-(-1);-1-3;2-2)=(-2;-4;-0)
По формуле ( см. скрин)
cos ∠ (vector{AB},vector{CN})=vector{AB}*vector{CN}/(|vector{AB}|*|vector{CN}|)
vector{AB}*vector{CN}=2*(-2)+(-4)*(-4)+(-2)*(0)=-4+16=12
|vector{AB}|=sqrt(2^2+(-4)^2+(-2)^2)=sqrt(24)=2sqrt(6)
|vector{CN}|=sqrt((-2)^2+(-4)^2+(0)^2)=sqrt(20)=2sqrt(5)
cos ∠ (vector{AB},vector{CN})=12/(2sqrt(6)*2sqrt(5)=sqrt(6)/2sqrt(5)
∠ (vector{AB},vector{CN})=arccos(sqrt(6)/2sqrt(5))