Question

已知向量ab满足a等于根号三b=2

已知向量a向量b满足|a|=1,|b|=根号3,a＋b=(根号3,1)求（1)|a＋b|(2)|a－b|(3)向量a＋b和向量a－b的夹角

Answer 1

1.|a+b|=2(太简单了) 2.|a-b|^2=a^2-2ab+b^2 |a+b|=2 a^2+2ab+b^2=4 ab=0 |a-b|^2=a^2-2ab+b^2=4 |a－b|=23.cosa=(a+b)(a-b)/|a-b||a+b|=a^2-b^2/4 =-1/2 a∈[0,π],a=2π/3