Find the coordinates of the points which trisect the line segment joining the points P (4, 2, - 6) and Q (10, - 16, 6)

Solution:

A point of trisection of a line segment divides it into 3 equal parts. i.e., it divides the line segment either in the ratio 1 : 2 or in the ratio 2 : 1.

Let A and B be the points that trisect the line segment joining the points P (4, 2, - 6) and Q (10, - 16, 6) in the ratios 1 : 2 and 2 : 1 respectively.

• Point A divides PQ in the ratio 1: 2 .
  Therefore, by section formula, the coordinates of point A are given by
  [(1(10) + 2(4))/(1 + 2), (1(- 16) + 2(2))/(1 + 2), (1(6) + 2(- 6))/(1 + 2)] = (6, - 4, - 2)
   
• Point B divides PQ in the ratio 2 :1.
  Therefore, by section formula, the coordinates of point B are given by 
  [(2(10) + 1(4))/(1 + 2), (2(- 16) + 1(2))/(1 + 2), (2(6) + 1(- 6))/(1 + 2)] = (8, - 10, 2)

NCERT Solutions Class 11 Maths Chapter 12 Exercise 12.3 Question 5

Find the coordinates of the points which trisect the line segment joining the points P (4, 2, - 6) and Q (10, - 16, 6)

Summary:

(6, - 4, - 2) and (8, - 10, 2) are the points that trisect the line segment joining the points P (4, 2, - 6) and Q (10, - 16, 6)