Find the ratio in which the YZ-plane divides the line segment formed by joining the points

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).

Solution:

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

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

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

$\Rightarrow 3 k-2=0$

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

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