Question

设单位向量a,b满足|3a-2b|=根号7,(1)求a,b的夹角,(2)求|3a+b|的值

Answer 1

(1) |3a-2b|=√7 (3a-2b)^2=7 ab=1/2

cos=ab/|a||b|=1/2 = 60°

(2) |3a+b|^2=9|a|^2+6ab+|b|^2=9+3+1=13 |3a+b|=√13