查找在另外两个向量之间创建特定角度的向量

问：

给定点 A、点 B、点 J 和角度 X，找到角度 ACB 等于 X 的每个点 C。这一切都在 3D 空间中，其中点 J 与 A 和 B 形成一个平面，因此所有解 C 都应该位于该平面上。

解决方案点 C 从未给我正确的角度。另外，当 X=90 时有多少个解？X！=90怎么样？

def angle_between_vectors(v1, v2):
    # Calculate the angle between two vectors in degrees
    angle_rad = np.arccos(np.dot(v1, v2) / (np.linalg.norm(v1) * np.linalg.norm(v2)))
    return np.degrees(angle_rad)

def find_points_with_angle_3d(A, B, J, X):

    # J forms a plane with A and B on which any solution C must lie
    # X is the angle (degrees) at which any solution C should make with A and B

    # set A, B, J as vectors
    A = np.array(A)
    B = np.array(B)
    J = np.array(J)

    # calculate vectors AB and AJ
    AB = B - A
    AJ = J - A

    # unit vector AB
    uAB = AB / np.linalg.norm(AB)

    # normal vector of the plane
    N = np.cross(AB, AJ)

    # unit vector N
    uN = N / np.linalg.norm(N)

    # project AJ onto plane
    AJ_proj = np.dot(AJ, uN) * uN

    # vector orthogonal to N and AB
    perpendicular_vector = np.cross(uN, AB)

    C1 = A + math.cos(np.radians(X)) * AJ_proj + math.sin(np.radians(X)) * perpendicular_vector

    C2 = A + math.cos(np.radians(X)) * AJ_proj - math.sin(np.radians(X)) * perpendicular_vector

    print("C1:", C1)
    print("C2:", C2)

    # Calculate angles ACB for C1 and C2
    AC1 = C1 - A
    BC1 = C1 - B
    angle_C1 = angle_between_vectors(AC1, BC1)

    AC2 = C2 - A
    BC2 = C2 - B
    angle_C2 = angle_between_vectors(AC2, BC2)

    print("Angle ACB for C1:", angle_C1)
    print("Angle ACB for C2:", angle_C2)

    return C1, C2

A = (2, 1, 3)
B = (4, 5, 4)
J = (7, 7, 7)
angle_X_deg = 45
C1, C2 = find_points_with_angle_3d(A, B, J, angle_X_deg)

输出：

C1: [ 3.55904966 -0.39776866  5.47297532]
C2: [0.44095034 2.39776866 0.52702468]
Angle ACB for C1: 54.735610317245346
Angle ACB for C2: 54.735610317245346