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
Correct Answer: C
Solution :
Let xy-plane divides the line joining the points \[(-1,\,3,\,4)\] and \[(2,\,-5,\,6)\] in \[\lambda :1\]. Then, \[z=\frac{{{m}_{1}}{{z}_{2}}+{{m}_{2}}{{z}_{1}}}{{{m}_{1}}+{{m}_{2}}}\]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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