Let the point P divides AB in the ratio k : 1.

Then,

Comparing this information with the details given in the question, we have

x₁ = 2, y₁ = -3, z₁ = 4; x₂ = -1, y₂ = 2, z₂ = 1 and m = k, n = 1

By section formula,

We know that the coordinates of the point R which divides the line segment joining two points P (x₁, y₁, z₁) and Q (x₂, y₂, z₂) internally in the ratio m : n is given by:

So, we have,

The coordinates of P =

Now, we check if for some value of k, the point coincides with the point C.

Put

⇒ -k + 2 = 0 ⇒ k = 2

When k =2, then

And

Therefore, C is a point which divides AB in the ratio 2 : 1 and is same as P.

Hence, A, B, C are collinear.