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  4. What is the ratio in which the line segment joining the points (-3 , 2 , 5) and (6 , 3 , 2) is divided by the XY - plane?

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Q. What is the ratio in which the line segment joining the points $ (-3 $ , $ 2 $ , $ 5) $ and $ (6 $ , $ 3 $ , $ 2) $ is divided by the $ XY $ - plane?

J & K CETJ & K CET 2019

Solution:

Let $P$ divides the line segment joining the points $(-3,2,5)$ and $(6, 3,2)$ in the ratio $k : 1$.
So, coordinates of $P$ are $\left(\frac{6k-3}{k+1}, \frac{3k+2}{k+1}, \frac{2k+5}{k+1}\right)$.
Now, $P$ lies on plane $z = 0$.
$[\because $ Equation of $XY$ plane is $Z= 0$]
$\therefore \frac{2k+5}{k+1} = 0$
$\Rightarrow k = -\frac{5}{2}$ or $ 5 : 2$ externally.