向量|a|=1,|b|=2,|c|=3,且向量a,b,c兩兩的夾角都是120度,
則a•b=-1,b•c=-3,c•a=-3/2.
（1）(2a+3c)(b+2c)=2a•b+4 c•a+3 b•c+6c^2
=37.
(2)|a+b+c|^2=a^2+b^2+c^2+2a•b+2 c•a+2 b•c
=3,
|a+b+c|=√3.
(3) (a+b+c)•c=a•c+b•c+c^2=9/2.
設(shè)a+b+c與c所成的夾角為θ,
則cosθ=(a+b+c)•c/[|a+b+c||c|]
=(9/2)/( 3√3)
=√3/2,
θ=π/6.