Three Dimensional Geometry Question 314
Question: If P (3, 2, - 4), Q (5, 4, - 6) and R (9, 8, -10) are collinear, then R divides PQ in the ratio
Options:
A) 3 :2 internally
B) 3:2 externally
C) 2:1 internally
D) 2:1 externally
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Suppose R divides PQ in the ratio $ \lambda :1 $ . Then, the coordinates of R are $ ( \frac{5\lambda +3}{\lambda +1},\frac{4\lambda +2}{\lambda +1},\frac{-6\lambda -4}{\lambda +1} ) $ But, the coordinates of R are given as (9, 8, -10)
$ \therefore \frac{5\lambda +3}{\lambda +1}=9,\frac{4\lambda +2}{\lambda +1}=8 $ and $ \frac{-6\lambda -4}{\lambda +1}=-10\Rightarrow \lambda =-\frac{3}{2} $ Hence, R divides PQ externally in the ratio 3 : 2
BETA
