Question

已知a,b为两个不共线的单位向量,k为实数,若向量a＋b与向量ka-b垂直,则k＝

Answer 1

(a+b)⊥(ka-b)(a+b)·(ka-b)=0ka^2+(k-1)ab-b^2=0k+(k-1)cos

-1=0(k-1)(1-cos

)=01-cos

≠0所以,(k-1)=0k=1