如圖所示，我們要計算任意兩個向量之間的夾角。
（圖中的座標數字是估計值，隨手給定）

python程式碼如下

import math 

AB = [1,-3,5,-1]
CD = [4,1,4.5,4.5]
EF = [2,5,-2,6]
PQ = [-3,-4,1,-6]

def angle(v1, v2):
    dx1 = v1[2] - v1[0]
    dy1 = v1[3] - v1[1]
    dx2 = v2[2] - v2[0]
    dy2 = v2[3] - v2[1]
    angle1 = math.atan2(dy1, dx1)
    angle1 =
 
 int(angle1 * 180/math.pi)
    # print(angle1)
    angle2 = math.atan2(dy2, dx2)
    angle2 = int(angle2 * 180/math.pi)
    # print(angle2)
    if angle1*angle2 >= 0:
        included_angle = abs(angle1-angle2)
    else:
        included_angle = abs(angle1) + abs(angle2)
        if included_angle >
 
 180:
            included_angle = 360 - included_angle
    return included_angle

ang1 = angle(AB, CD)
print("AB和CD的夾角")
print(ang1)
ang2 = angle(AB, EF)
print("AB和EF的夾角")
print(ang2)
ang3 = angle(AB, PQ)
print("AB和PQ的夾角")
print(ang3)
ang4 = angle(CD, EF)
print("CD和EF的夾角")
print(ang4)
ang5 = angle(CD,
 
 PQ)
print("CD和PQ的夾角")
print(ang5)
ang6 = angle(EF, PQ)
print("EF和PQ的夾角")
print(ang6)

結果為

AB和CD的夾角
55
AB和EF的夾角
139
AB和PQ的夾角
52
CD和EF的夾角
84
CD和PQ的夾角
107
EF和PQ的夾角
169