Find the ratio in which the yz-plane divides the line segment formed by joining the points (- 2, 4,7) and (3, - 5, 8).

The given points are A(-2,4,7 ) and B(3,- 5, 8). Let the point P (0, y, z) in yz-plane divides AB in the ratio k:1, then

r-coordinate of point $\mathrm{P}=\frac{{\mathrm{mx}}_2+{\mathrm{nx}}_1}{\mathrm{m}+\mathrm{n}}$

$\frac{\mathrm{k}\times 3+1\times (-2)}{\mathrm{k}+1}=0[\because \mathrm{x}-\mathrm{coordinate} \mathrm{of} \mathrm{p} \mathrm{is} \mathrm{zero}]$

$\begin{array}{l}\Rightarrow \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}3\mathrm{k}-2\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}=0\Rightarrow \mathrm{k}=\frac{2}{3}\\ \Rightarrow \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\mathrm{k}:1\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}=2:3\end{array}$

yz-plane divides the segment internally in the ratio 2:3.