Find the ratio in which the YZ-plane divides the line segment formed by joining the points (- 2, 4, 7) and (3, - 5, 8)

Solution:

Let the YZ plane divide the line segment joining points (- 2, 4, 7) and (3, - 5, 8) in the ratio k : 1

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

[(k(3) - 2)/(k + 1), (k(- 5) + 4)/(k + 1), (k(8) + 7)/(k + 1)]

On the YZ plane, the x - coordinate of any point is zero.

⇒ (3k - 2)/(k + 1) = 0

⇒ 3k - 2 = 0

⇒ k = 2/3

Thus, the YZ-plane divides the line segment formed by joining the given points in the ratio 2 : 3

NCERT Solutions Class 11 Maths Chapter 12 Exercise 12.3 Question 3

Find the ratio in which the YZ-plane divides the line segment formed by joining the points (- 2, 4, 7) and (3, - 5, 8).

Summary:

The YZ-plane divides the line segment formed by joining the points (- 2, 4, 7) and (3, - 5, 8) in the ratio 2:3