Question

已知平面向量a和b |a|=1 |b|=2 且a与b的夹角为120度 则| 2 a+b| 等于

Answer 1

解：∵|2a+b|^2=4a^2+4ab+b^2=4*1^2+4*1*2*cos120°+2^2=4-4+4=4
∴|2a+b|=2

Answer 2

a*b=|a||b|cos120=1*2*(-1/2)=-1
|2a+b|^2=4a^2+4a*b+b^2=4-4+4=4
|2a+b|=2

Answer 3

| 2 a+b| =|2a| |b|sina=2*2*sin120=2根号3