Three Dimensional Geometry Question 189
Question: The xy-plane divides the line joining the points (?1, 3, 4) and (2, ?5, 6)
[RPET 2000]
Options:
A) Internally in the ratio 2 : 3
B) Internally in the ratio 3 : 2
C) Externally in the ratio 2 : 3
D) Externally in the ratio 3 : 2
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Answer:
Correct Answer: C
Solution:
Let xy-plane divides the line joining the points $ (-1,,3,,4) $ and $ (2,,-5,,6) $ in $ \lambda :1 $ . Then, $ z=\frac{m_1z_2+m_2z_1}{m_1+m_2} $
Þ $ z=\frac{6\lambda +4}{\lambda +1} $ For xy-plane, $ z=0 $
$ \Rightarrow 0=\frac{6\lambda +4}{\lambda +1} $
$ \Rightarrow \lambda =-2/3=-2:3 $ Externally in the ratio 2 : 3. Trick : Ratio = $ \frac{-z_1}{z_2} $ = $ \frac{-4}{6} $ = $ \frac{-2}{3} $ Externally in the ratio 2 : 3.
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