Three Dimensional Geometry Question 348
Question: Ratio in which the zx-plane divides the join of (1, 2 3) and (4, 2, 1).
Options:
A) 1:1 internally
B) 1:1 externally
C) 2:1 internally
D) 2: 1 externally
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Suppose zx-plane divides the join of (1, 2, 3) and (4, 2, 1) in the ratio $ \lambda :1. $ Then, the co-ordinates of the point of division are $ ( \frac{4\lambda +1}{\lambda +1},\frac{2\lambda +2}{\lambda +1},\frac{\lambda +3}{\lambda +1} ) $ This point lies on zx-plane
$ \therefore $ y-coordinate $ =0\Rightarrow \frac{\lambda +2}{\lambda +1}=0\Rightarrow \lambda =-1 $ Hence, zx-plane divides the join of (1, 2, 3) and (4, 2, 1) externally in the ratio 1:1. Aliter We know that the zx-plane divides the segment joining $ P(x_1,y_1,z_1) $ and $ Q(x_2,y_2,z_2) $ in the ratio $ -y_1:y_2 $ .
$ \therefore $ zx-plane divides the join of (1, 2, 3) and (4, 2, 1) in the ratio - 2 : 2 i.e., 1:1 externally.
BETA
