A point R with x - coordinate 4 lies on the line segment joining the points P (2, - 3, 4) and Q (8, 0, 10). Find the coordinates of the point R.
[Hint: Suppose R divides PQ in the ratio k : 1. The coordinates of the point R are given by ((8k + 2)/(k + 1), (- 3)/(k + 1), (10k + 4)/(k + 1))]

Solution:

The coordinates of points P and Q are given as P (2, - 3, 4) and Q (8, 0, 10).

Let R divide the line segment PQ in the ratio k : 1.

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

[(k(8) + 2)/(k + 1), (k(0)- 3)/(k + 1), (k(10) + 4)/(k + 1)]

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

It is given that the x - coordinate of point R is 4

Hence,

(8k + 2)/(k + 1) = 4

8k + 2 = 4k + 4

4k = 2

k = 1/2

Therefore, the coordinates of point R are

[4, (- 3)/(1/2 + 1), (10(1/2) + 4)/(1/2 + 1)]

⇒ (4, - 2, 6)

Thus, the coordinates of point R are (4, - 2, 6)

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NCERT Solutions Class 11 Maths Chapter 12 Exercise ME Question 5

A point R with x - coordinate 4 lies on the line segment joining the points P (2, - 3, 4) and Q (8, 0, 10). Find the coordinates of the point R. [Hint: Suppose R divides PQ in the ratio k : 1. The coordinates of the point R are given by ((8k + 2)/(k + 1), (- 3)/(k + 1), (10k + 4)/(k + 1))]

Summary:

The coordinates of the point R when R with x - coordinate 4 lies on the line segment joining the points P (2, - 3, 4) and Q (8, 0, 10) are (4, -2, 6)