Question

若向量ab满足|a|=1,|b|=2,且a与b的夹角为派/3,则|2a+b|=

Answer 1

｜2a+b｜^2=4a^2+4ab+b2,

a^2=|a|^2=1, b^2=|b|^2=4,

4*a*b=4*|a|*|b|*cosπ/3=4*1*2*1/2=4

所以｜2a+b｜^2=4a^2+4ab+b2=4+4+4=12, |2a+b|=2√3