已知向量a=(3,-2),b=(2,-3)求向量a+b与a-b的夹角
已知向量a=(3,-2),b=(2,-3)求向量a+b与a-b的夹角
数学人气:989 ℃时间:2020-01-26 14:14:06
优质解答
a+b=(5,-5),a-b=(1,1),则cosθ=[(a+b)*(a-b)]/[|a-b||a+b|],(a+b)*(a-b)=a²-b²=|a|²-|b|²=0,|a-b||a+b|=(5√2)(√2)=10,所有cosθ=0,夹角为90°.
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