已知│a│=2,│b│=1,a与b的夹角为Л/3,求向量a+b与a-b的夹角的余弦值
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let a+b与a-b的夹角 =x
|a+b|^2
= |a|^2+|b|^2 +2|a||b|cosπ/3
= 4 +1 + 2(2)(1)(1/2)
= 7
|a+b| =√7
|a-b|^2 = |a|^2+|b|^2 -2|a||b|cosπ/3 = 3
|a-b|=√3
(a+b).(a-b) = |a|^2 -|b|^2 = 3 = |a+b||a-b|cosx
3 = √7.√3cosx
cosx = √21/7
|a+b|^2
= |a|^2+|b|^2 +2|a||b|cosπ/3
= 4 +1 + 2(2)(1)(1/2)
= 7
|a+b| =√7
|a-b|^2 = |a|^2+|b|^2 -2|a||b|cosπ/3 = 3
|a-b|=√3
(a+b).(a-b) = |a|^2 -|b|^2 = 3 = |a+b||a-b|cosx
3 = √7.√3cosx
cosx = √21/7
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