已知a,b是非零向量且满足（3a-b)垂直于a,(4a-b)垂直于b则a与b的夹角快,

Question

已知a,b是非零向量且满足（3a-b)垂直于a,(4a-b)垂直于b则a与b的夹角 快,

Answer 1

(3a-b)垂直于a => (3a-b)a=0 => |a|^2=(1/3)ab >=0 => |a|=[(1/3)^0.5](ab)^0.5
(4a-b)垂直于b => (4a-b)b=0 => |b|^2 =4ab >=0 => |b|=2(ab)^0.5
ab夹角 cos = (ab)/|a||b| = (ab)/{[2*(1/3)^0.5]ab} =3^0.5 / 2
所以 = 30度