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Question

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.

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Solution

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

Then coordinates of Q are

(9k+3k+1,8k+2k+1,10k4k+1)

But it is given that coordinates of Q is (5, 4, 6)

9k+3k+1=59k+3=5k+5

4k=2 k=12

Thus Q divides the line segment joining points P and R in the ratio 12 i.e. 1:2 internally.


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