Question

向量a+b+c=0,|a|=1,|b|=2,|c|=√2,则a*b+b*c+c*a的值是?

Answer 1

a+b+c=0

(a+b+c)^2=0

a*a+b*b+c*c+2(a*b+b*c+c*a)=0

|a|^2+|b|^2+|c|^2+2(a*b+b*c+c*a)=0

1+4+2+2(a*b+b*c+c*a)=0

a*b+b*c+c*a=-7/2