Using section formula, show that the points A(2, - 3, 4), B (- 1, 2, 1) and C(0, 1/3, 2) are collinear

Solution:

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

Hence, by section formula, the coordinates of point of intersection (P) are given by

P [(k(- 1) + 2)/(k + 1), (k(2) - 3)/(k + 1), (k(1) + 4)/(k + 1)]

Now, we find the value of k at which point P coincides with point C.

Let us set the x-coordinates of P and C equal.

By taking (- k + 2)/(k + 1) = 0, we obtain k = 2.

For k = 2, the coordinates of point P are (0, 1/3, 2) i.e., (0, 1/3, 2) is a point that divides AB internally in the ratio 2 : 1 and is the same as point C.

Hence, points A, B, and C are collinear

NCERT Solutions Class 11 Maths Chapter 12 Exercise 12.3 Question 4

Using section formula, show that the points A(2, - 3, 4), B (- 1, 2, 1) and C(0, 1/3, 2) are collinear

Summary:

We proved that the points A(2, - 3, 4), B (- 1, 2, 1) and C(0, 1/3, 2) are collinear by using the section formula