Question

设同一平面内的向量a,b,c的模均为1,且两两的夹角为120度.求证向量a垂直(b-c).

Answer 1

∵(b-c)*a=ab-ac= |a|.|b|.cos120°- |a|.|c|.cos120°=

1×1×cos120°- 1×1×cos120° = 0

∴ 向量a垂直(b-c)

∵作图分析可知：b+c=-a

∴|ka+b+c|=|(k-1)a|

∵a的模为1

∴|k-1|＞1,

∴k2