Question

已知a与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,求k

Answer 1

向量a+b与向量ka-b垂直 ==> (a+b) * (ka-b) = 0

==> k -a*b + ka*b - 1 = 0

==> (k-1)(a*b + 1) = 0, a*b + 1 > 0 (a与b为两个不共线的单位向量)

==> k = 1