Question

已知向量a=(1,2),b=(-2,-4),丨c丨=根号5，若（a+b）·c=5/2，则a与c的夹角为

Answer 1

a=(1,2),b=(-2,-4), a+b = (-1,-2) = -a
5/2 = (a+b)•c= - a•c = |a| |c| cos<a,c> = √5 * √5 cos<a,c>
=> cos<a,c> = 1/2
=> a与c的夹角为 60°

Answer 2

a=(1,2),b=(-2,-4), a+b = (-1,-2) = -a
5/2 = (a+b)•c= - a•c = -|a| |c| cos<a,c> = -√5 * √5 cos<a,c>
=> cos<a,c> =- 1/2
=> a与c的夹角为 120°
729707767他漏了负号