Question

|a|=1,|b|=2,c=a+b,且c⊥a,則向量a與b的夾角為(    )

A.30°              B.60°             C.120°             D.150°

Answer 1

解析:∵c⊥a,即(a+b)⊥a,

∴(a+b)·a=0.

∴|a|²+a·b=0.∴1+2cosθ=0.

∴cosθ=-.

又θ∈［0,180°］,∴θ=120°.

答案:C