Question

Find the ratio in which the line segment joining the points (4, 8, 10) and (6, 10, –8) is divided by the yz-plane.

Answer 1

Let A = (4, 8, 10) , B = (6, 10, $-$8)
Let the line joining A and B be divided by the YZ-plane at point P in the ratio $\lambda :1$.
∴ P=$\left(\frac{6\lambda +4}{\lambda +1},\frac{10\lambda +8}{\lambda +1},\frac{-8\lambda +10}{\lambda +1}\right)$
Since P lies on the YZ-plane, the x-coordinate of P will be zero.
$$\begin{gathered} \therefore \frac{6\lambda +4}{\lambda +1}=0 \\ \Rightarrow 6\lambda +4=0 \\ \Rightarrow 6\lambda =-4 \\ \therefore \lambda =\frac{-2}{3} \end{gathered}$$
Hence, the YZ-plane divides AB in the ratio 2:3 (externally)