المتجهات

# 3v = 3(1, -2, 0, 5) = (3, -6, 0, 15)
v = [1, -2, 0, 5]
scalar = 3
result = [scalar * entry for entry in v]
print(result)

u = [-3, -2, 0, -1, 4]
v = [-1, -1, 2, -3, 5]

if len(u) != len(v):
    raise ValueError("dimensions must match")

result = [u[i] + v[i] for i in range(len(u))]
print(result)

from math import sqrt

v = [-1, -3, 5, 3, 1, 2]
length_squared = sum(entry ** 2 for entry in v)
length = sqrt(length_squared)
print(length)

u = [-3, 4]
print("طول (-3, 4) =", sqrt(sum(e ** 2 for e in u)))  # 5.0

import matplotlib.pyplot as plt

def draw_vector(x, y, color, label):
    plt.annotate("", xy=(x, y), xytext=(0, 0),
                 arrowprops={"arrowstyle": "->", "color": color, "linewidth": 2})
    plt.text(x * 1.08, y * 1.08, label)

plt.figure(figsize=(5, 5), dpi=100)
draw_vector(1, 2, "#0D5C43", "v = (1,2)")
draw_vector(-3, 4, "#22C55E", "u = (-3,4)")
plt.axhline(0, color="#94a3b8", linewidth=0.8)
plt.axvline(0, color="#94a3b8", linewidth=0.8)
plt.xlim(-5, 5)
plt.ylim(-5, 5)
plt.grid(alpha=0.3)
plt.gca().set_aspect("equal", adjustable="box")
plt.show()