Find the ratio in which the line segment joining the points ( 4, 8, 10 ) and ( 6, 10, -8 ) is divided by the YZ- plane.

Dear Student,

$$\begin{gathered} \mathrm{Let} \mathrm{the} \mathrm{point} \mathrm{A}\left(4,8,10\right) \mathrm{and} \mathrm{point} \mathrm{B}\left(6,10,-8\right) \mathrm{is} \mathrm{divided} \mathrm{by} \mathrm{the} \mathrm{YZ}-\mathrm{plane} \mathrm{at} \mathrm{point} \mathrm{P} \mathrm{in} \mathrm{the} \mathrm{ratio} \mathrm{\lambda }:1 \\ \mathrm{So}, \\ \mathrm{Coordinate} \mathrm{of} \mathrm{point} \mathrm{P}=\left(\frac{6\mathrm{\lambda }+4}{\mathrm{\lambda }+1},\frac{10\mathrm{\lambda }+8}{\mathrm{\lambda }+1},\frac{-8\mathrm{\lambda }+10}{\mathrm{\lambda }+1}\right) \\ \mathrm{Since} \mathrm{point} \mathrm{R} \mathrm{lies} \mathrm{on} \mathrm{YZ} \mathrm{plane}, \mathrm{Therefore}, \mathrm{x}-\mathrm{coordinate}=0 \\ \Rightarrow \frac{6\mathrm{\lambda }+4}{\mathrm{\lambda }+1}=0 \\ \Rightarrow 6\mathrm{\lambda }+4=0 \\ \Rightarrow \mathrm{\lambda }=\frac{-4}{6} \\ \Rightarrow \mathrm{\lambda }=\frac{-2}{3} \\ \mathrm{Thus}, \mathrm{YZ} \mathrm{plane} \mathrm{divide} \mathrm{in} \mathrm{the} \mathrm{ratio} -2:3 \end{gathered}$$

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