1
a*b=x1*x2+y1*y2=-2*4-3*2=-8-6=-14
2
|a+b|=√(a+b)²=√(a²+2abcos60+b²)=√(1+2*1*1*1/2+1)=√3
3
cos(a∧b)=(x1x2+y1y2)/(√(x1²+y1²)*√(x2²+y2²)
-1/2a{-1/2x1;-1/2y1} -b{-x2;-y2}
cos((-1/2a)∧(-b))=(1/2x1x2+1/2y1y2)/(√1/4(x1²+y1²)*√(x2²+y2²)=
=1/2(x1x2+y1y2):1/2(√(x1²+y1²)*√(x2²+y2²)=
=(x1x2+y1y2)/(√(x1²+y1²)*√(x2²+y2²)=cos(a∧b)=-1/2
4
(λa+b)_|_b
λa+b{-λ+3;-4λ+2}
(λa+b)*b=(-λ+3)*3-2*(-4λ-2)=0
-3λ+9+8λ+4=0
5λ=-13
λ=-2,6