Question

Find the ratio in which the line joining (2, 4, 5) and (3, 5, 4) is divided by the yz-plane.

Answer 1

Let A $\equiv$ (2, 4, 5) and B $\equiv$ (3, 5, 4)

Let the line joining A and B be divided by the yz-plane at point P in the ratio $\lambda :1$

Then, we have :

P $\equiv (\frac{3\lambda +2}{\lambda +1},\frac{5\lambda +4}{\lambda +1},\frac{4\lambda +5}{\lambda +1})$

Since P lies on the yz-plane, the x-coordinates of P will be zero.

$\therefore \frac{3\lambda +2}{\lambda +1}=0$

$\Rightarrow 3\lambda +2=0$

$\Rightarrow \lambda =\frac{-2}{3}$