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 $k:1$.

Hence, by 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.

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

$3k-2=0$

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

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