Question

已知|a|=3,|b|=4,且a与b不共线,k为何值时,向量a+kb与a-kb互相垂直

Answer 1

向量a+kb与a-kb互相垂直时,有

0 = (a+kb)*(a-kb) = a*a + kb*a - ka*b - k^2b*b = |a|^2 - k^2|b|^2

= 3^2 - k^2*4^2,

k^2 = 3^2/4^2,

k = 3/4

或

k = -3/4