设a=3i-j-2k,b=i+2j-k,求a与b的夹角余弦{答案是cos(a,b)=3/(2√21)}求步骤

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/16 07:53:49
设a=3i-j-2k,b=i+2j-k,求a与b的夹角余弦{答案是cos(a,b)=3/(2√21)}求步骤设a=3i-j-2k,b=i+2j-k,求a与b的夹角余弦{答案是cos(a,b)=3/(2

设a=3i-j-2k,b=i+2j-k,求a与b的夹角余弦{答案是cos(a,b)=3/(2√21)}求步骤
设a=3i-j-2k,b=i+2j-k,求a与b的夹角余弦{答案是cos(a,b)=3/(2√21)}求步骤

设a=3i-j-2k,b=i+2j-k,求a与b的夹角余弦{答案是cos(a,b)=3/(2√21)}求步骤
cos(a,b)=/(|a|*|b|)
其中为a和b的内积,|a|,|b|分别为a和b的模.
=3*1+(-1)*2+(-2)*(-1)=3
|a|=√(3^2+(-1)^2+(-2)^2)=√14
|b|=√(1^2+2^2+(-1)^2)=√6
所以cos(a,b)=/(|a|*|b|)=3/(√14*√6)=3/(2√21)