Question

设平面上向量a等于(cosa,sina)b等于(负的二分之一,二分之根号三)求向量a加向量b与向量a减b垂直

Answer 1

a+b=(cosA-1/2,sinA+√3\2)
a-b=(cosA+1/2,sinA-√3\2)

则(a+b)·(a-b)
=(cosA-1/2)(cosA+1/2)+(sinA+√3\2)(sinA-√3\2)
=(cosA)^2-1/4+(sinA)^2-3/4
又因为 (cosA)^2 + (sinA)^2 = 1
所以
=1-1
=0
所以向量a加向量b与向量a减b垂直

提醒：题中的a,b上要加箭头

求采纳

Answer 2

(a+b).(a-b)
=(cosa-1/2,sina+√3/2).(cosa+1/2,sina-√3/2)
=(cosa)^2 - 1/4 + (sina)^2 - 3/4
=1 - 1/4 - 3/4
= 0
=> (a+b)与a-b) 垂直