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Q.
The ratio in which YZ-plane divides the line segment formed by joining the points $(-2,4,7)$ and $(3,-5,8)$, is
Introduction to Three Dimensional Geometry
Solution:
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.
$x$ -coordinate of point $P=\frac{m x_{2}+n x_{1}}{m+ n}$
$\frac{ k \times 3+1 \times(-2)}{ k +1}=0$
($\because x$ -coordinate of $P$ is zero)
$\Rightarrow 3 k -2=0$
$\Rightarrow k =\frac{2}{3}$
$\Rightarrow k : 1=2: 3$
$\therefore $ YZ-plane divides the segment internally in the ratio $2: 3$
