Q3 of 25 Page 277

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

Let the line segment formed by joining the points P (-2, 4, 7) and Q (3, -5, 8) be PQ.

We know that any point on the YZ-plane is of the form (0, y, z).


Now, let R (0, y, z) divides the line segment PQ in the ratio k : 1.


Then,


Comparing this information with the details given in the question, we have


x1 = -2, y1 = 4, z1 = 7; x2 = 3, y2 = -5, z2 = 8 and m = k, n = 1


By section formula,


We know that the coordinates of the point R which divides the line segment joining two points P (x1, y1, z1) and Q (x2, y2, z2) internally in the ratio m : n is given by:



So, we have




⇒ 3k – 2 = 0 ⇒ 3k = 2



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


More from this chapter

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1

Find the coordinates of the point which divides the line segment joining the points (– 2, 3, 5) and (1, – 4, 6) in the ratio (i) 2 : 3 internally, (ii) 2 : 3 externally.

 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.

 4

Using section formula, show that the points A (2, –3, 4), B (–1, 2, 1) and are collinear.

5

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