import math
print("===== 题目3 向量运算 =====")
A = [3, 4]
B = [1, 2]
A_plus_B = [a + b for a, b in zip(A, B)]
print(f"A + B = {A_plus_B}")
two_A = [2 * a for a in A]
print(f"2 * A = {two_A}")
norm_A = math.sqrt(sum(x**2 for x in A))
print(f"A的模长 = {norm_A}")
print("\n===== 题目4 点积 & 余弦相似度 =====")
A1 = [1, 2, 3]
B1 = [4, 5, 6]
dot1 = sum(a*b for a, b in zip(A1, B1))
norm_A1 = math.sqrt(sum(x**2 for x in A1))
norm_B1 = math.sqrt(sum(x**2 for x in B1))
cos1 = dot1 / (norm_A1 * norm_B1)
print(f"A1·B1 点积 = {dot1}")
print(f"A1、B1 余弦相似度 = {cos1:.4f}")
A2 = [1, 0]
B2 = [0, 1]
dot2 = sum(a*b for a, b in zip(A2, B2))
norm_A2 = math.sqrt(sum(x**2 for x in A2))
norm_B2 = math.sqrt(sum(x**2 for x in B2))
cos2 = dot2 / (norm_A2 * norm_B2)
print(f"\nA2·B2 点积 = {dot2}")
print(f"A2、B2 余弦相似度 = {cos2}")
print("原因：两向量正交（夹角90°），余弦值为0")