已知向量a,b的夹角为120°,且|a|=3,|b|=1,则|a-2b|==根号13?

Question

已知向量a,b的夹角为120°,且|a|=3,|b|=1,则|a-2b|=
=根号13?

Answer 1

|a-2b|= √[(a-2b)]^2=√[a^2-4a*b+4b^2]
=√[|a|^2]-4|a|*|b|*cos120°+4|b^2|]
=√[9-4*3*1*(-1/2)+4]=√19