Question

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.

Answer 1

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)