设a,b向量满足丨a丨=丨b丨=1,且丨3a-b丨=根号7.求2a+b与b的夹角.求丨3a+b丨/丨3a-b丨.

题目

设a,b向量满足丨a丨=丨b丨=1,且丨3a-b丨=根号7.求2a+b与b的夹角.求丨3a+b丨/丨3a-b丨.

答案

设a,b的夹角=x
|3a-b| = √7
9|a|^2+|b|^2-6|a||b|cosx = 7
10-6cosx=7
cosx = 1/2
x= π/3
|3a+b|^2 = 9|a|^2+|b|^2+6|a||b|cosx
= 9+1+3
=13
|3a+b|/|3a-b| = √(13/7)