Show that the plane `a x+b y+c z+d=0` divides the line joining the points `(x_1, y_1, z_1)a n d(x_2, y_2, z_2)` in the ratio `(a x_1+b y_1+c z_1+d)/(a x_2+b y_2+c z_2+d)` .

Explanation

To show that the plane \( ax + by + cz + d = 0 \) divides the line joining the points \( (x_1, y_1, z_1) \) and \( (x_2, y_2, z_2) \) in the ratio

\[ \frac{ax_1 + by_1 + cz_1 + d}{ax_2 + by_2 + cz_2 + d}, \]

we will follow these steps:

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