已知向量a=(1,2),b=(-2,-4),丨c丨=根号5,若(a+b)·c=5⼀2,则a与c的夹角为

2025-06-21 09:04:57
推荐回答(2个)
回答1:

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

回答2:

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