非零向量a、b满足|a+b|=|a-b|,则a与b的夹角为多少度?
问题描述：
非零向量a、b满足|a+b|=|a-b|,则a与b的夹角为多少度?
答
|a+b| = |a-b|
=> |a+b|^2 = |a-b|^2
|a+b|^2 = (a+b).(a+b) = |a|^2+|b|^2 + 2|a||b| cosθ
|a-b|^2 = (a-b).(a-b) = |a|^2+|b|^2 - 2|a||b| cosθ
=>|a||b| cosθ =0
θ = 90°