Given that P (3, 2, - 4), Q (5, 4, - 6) and R (9, 8, - 10) are collinear. Find the ratio in which Q divides PR

Solution:

Let point Q (5, 4, - 6) divides the line segment joining points P (3, 2, - 4) and R (9, 8, - 10) in the ratio k : 1.

Therefore, by section formula,

(5, 4, - 6) = [(k(9) + 1(3))/(k + 1), (k(8) + 1(2))/(k + 1), (k(- 10) + (-4)(1))/(k + 1)]

Hence,

(9k + 3)/(k + 1) = 5

9k + 3 = 5k + 5

4k = 2

k = 2/4

k = 1/2

Thus, point Q divides PR in the ratio 1: 2

NCERT Solutions Class 11 Maths Chapter 12 Exercise 12.3 Question 2

Given that P (3, 2, - 4), Q (5, 4, - 6) and R (9, 8, - 10) are collinear. Find the ratio in which Q divides PR

Summary:

Point Q (5, 4, - 6) divides P (3, 2, - 4) × R (9, 8, - 10) in the ratio 1: 2