Show that the three points `A(2,3,4),\ B(-1,2,-3)a n d\ C(-4,1,-10)` are collinear and find the ratio in which C divides AB.

Explanation

To show that the points \( A(2, 3, 4) \), \( B(-1, 2, -3) \), and \( C(-4, 1, -10) \) are collinear and to find the ratio in which \( C \) divides \( AB \), we can use the section formula.

### Step 1: Understand the Section Formula
The section formula in 3D states that if a point \( C \) divides the line segment \( AB \) in the ratio \( m:n \), then the coordinates of point \( C \) can be expressed as:
\[ C\left(\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}, \frac{mz_2 + nz_1}{m+n}\right) \]
where \( A(x_1, y_1, z_1) \) and \( B(x_2, y_2, z_2) \).
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