Question

Find the ratio in which the line segment, joining the points P(2, 3, 4) and Q(-3, 5, -4) is divided by the yz-plane. Also, find the point of intersection.

Answer 1

Let PQ be the divided by the yz-plane at a point R in the ratio $\lambda :1$.

Then, the coordinates of R are

$(\frac{-3\lambda +2}{\lambda +1},\frac{5\lambda +3}{\lambda +1},\frac{-4\lambda +4}{\lambda +1})$ ...(i)

Since R lies on the yz-plane, the x-coordinate or R is therefore 0.

$\therefore \frac{-3\lambda +2}{\lambda +1}=0$, or $\lambda =\frac{2}{3}$.

So, the required ratio is $\frac{2}{3}:1,$ i.e., 2:3.

Putting $\lambda =\frac{2}{3}$ in (i), the point of intersection of the line segemnt PQ and the yz-plane is $(0,\frac{19}{5},\frac{4}{5})$.