A) 1:1 internally
B) 1:1 externally
C) 2:1 internally
D) 2: 1 externally
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 \[\left( \frac{4\lambda +1}{\lambda +1},\frac{2\lambda +2}{\lambda +1},\frac{\lambda +3}{\lambda +1} \right)\] 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.
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