Question

已知向量a,b满足丨a丨=3 丨b丨=4,a与b的夹角为120°,则丨a+2b丨=?

Answer 1

|a|=3,|b|=4,=2π/3

则：a·b=|a|*|b|*cos(2π/3)=-6

|a+2b|^2=|a|^2+4|b|^2+4a·b

=9+64-24

=49

即：|a+2b|=7