Question

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

Answer 1

Let the $YZ$ plane divide the line segment joining points $(-2,4,7)$ and $(3,-5,8)$ in the ratio $k:1$.

Using section formula, the coordinates of point of intersection are given by,

$(\frac{k\left(3\right)-2}{k+1},\frac{k(-5)+4}{k+1},\frac{k\left(8\right)+7}{k+1})$

On the $YZ$ plane, the $x$-coordinate of any point is zero.

$\frac{3k-2}{k+1}=0$

$\Rightarrow 3k-2=0$

$\Rightarrow k=\frac{2}{3}$

Thus the $YZ$ plane divides the line segment formed by joining the given points in the ratio $2:3$.