工作中遇到两平面求相交直线方程的问题：

已知两个平面的方程为：

平面 1： 15274.32X + 16334.64Y + 3910347.7Z -1217342147660.14 = 0

平面 2： -14272.59X + -32556.69Y + 3899632.2Z + 1993749987653.63 = 0

如何何求点向式的直线方程？

我问了 chatGPT 代码如下：

def line_intersect(p1, p2):
    """
    Finds the line of intersection between two planes given their equations in the form ax + by + cz = d.
    Returns the direction vector of the line and a point on the line.
    """
    a1, b1, c1, d1 = p1
    a2, b2, c2, d2 = p2
    # Compute the direction vector of the line of intersection
    direction = (b1 * c2 - b2 * c1, a2 * c1 - a1 * c2, a1 * b2 - a2 * b1)
    # Find a point on the line of intersection
    x = (b1 * d2 - b2 * d1) / (a1 * b2 - a2 * b1)
    y = (a2 * d1 - a1 * d2) / (a1 * b2 - a2 * b1)
    z = 0
    if c1 != 0:
        z = d1 / c1
    elif c2 != 0:
        z = d2 / c2
    return direction, (x, y, z)

我数学基础较差，都不知道给的答案对不对，恳请各位大佬给解答一下，谢谢。