A) internally in the ratio \[2:3\]
B) externally in the ratio\[2:3\]
C) internally in the ratio\[3:2\]
D) externally in the ratio\[3:2\]
Correct Answer: B
Solution :
Suppose\[xy-\]plane divides at the line joining the given points in the ratio\[\lambda :1\]. The coordinates of the points of division are \[\left[ \frac{2\lambda -1}{\lambda +1},\frac{-5\lambda +3}{\lambda +1},\frac{6\lambda +4}{\lambda +1} \right]\]. The points lies on the\[xy-\]plane. \[\therefore \] \[\frac{6\lambda +4}{\lambda +1}=0\Rightarrow \lambda =\frac{-2}{3}\]
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