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  4. The ratio in which ZX-plane divides the line segment AB joining the points A(4,2,3) and B(-2,4,5) is equal to

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Q. The ratio in which ZX-plane divides the line segment AB joining the points $ A(4,2,3) $ and $ B(-2,4,5) $ is equal to

J & K CETJ & K CET 2011Introduction to Three Dimensional Geometry

Solution:

Let $ \lambda :1 $ be the ratio in which ZX-plane divides the line segment AB. Day By section formula
$ =\left( \frac{2\lambda +4}{\lambda +1},\frac{4\lambda +2}{\lambda +1},\frac{5\lambda +3}{\lambda +1} \right) $
For ZX-plane Cording of $ y=0 $
$ \frac{4\lambda +2}{\lambda +1}=0 $
$ \Rightarrow $ $ \lambda =-1/2 $
$ \Rightarrow $ $ \lambda :1=-1:2 $
Hence, ZX-plane i.e., point P divides the line segment AB in the ratio $ 1:2 $ externally.