（1）已知非0向量a,b满足|a|=|b|=|a-b|,求a与a+b的夹角.（2）设|a|=|b|=1,|3a-2b|=3,求|3a+b|

Question

（1）已知非0向量a,b满足|a|=|b|=|a-b|,求a与a+b的夹角.（2）设|a|=|b|=1,|3a-2b|=3,求|3a+b|

Answer 1

(1).已知非0向量a,b满足|a|=|b|=|a-b|,求a与a+b的夹角.设a=(m,0)(其中m>0),b=(mcosφ,msinφ)；则a-b=(m(1-cosφ),-msinφ)；|a-b|=√[m²(1-cosφ)²+m²sin²φ]=m√(2-2cosφ)=|a|=m故得2-2cosφ...