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Question

Mathematics Question on introduction to three dimensional geometry

Given that the points P(3,2,−4)P(3,2, - 4) , Q(5,4,−6)Q(5,4, - 6) and R(9,8,−10)R(9,8,-10) are collinear, the ratio in which QQ divides PRPR externally is

A

1:21:2

B

2:12:1

C

1:11:1

D

2:22:2

Answer

1:21:2

Explanation

Solution

Let QQ divides PRPR externally in K:1K : 1

By external section formula, we get
5=9×K−1×3K−15 = \frac{9 \times K - 1\times 3}{K-1}
⇒5K−5=9K−3\Rightarrow 5K - 5 = 9K - 3
⇒5K−9K=−3+5\Rightarrow 5K - 9K = - 3 + 5
⇒−4K=2\Rightarrow - 4K = 2
⇒K=−24\Rightarrow K = - \frac{2}{4}
⇒K=−12\Rightarrow K = - \frac{1}{2}
Hence, QQ divides PRPR in the ratio 1:21 : 2 (externally).