Question

The ratio in which the line joining (2, 4, 5) and (3, 5, –9) is divided by the yz-plane is
(a) 2 : 3
(b) 3 : 2
(c) –2 : 3
(d) 4 : –3

Answer 1

(c) $-$2 : 3

Let A$\equiv$(2, 4, 5) and B$\equiv$(3, 5, $-$9)
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$\equiv \left(\frac{3\lambda +2}{\lambda +1},\frac{5\lambda +4}{\lambda +1},\frac{-9\lambda +5}{\lambda +1}\right)$

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

$$\begin{gathered} \therefore \frac{3\lambda +2}{\lambda +1}=0 \\ \Rightarrow 3\lambda +2=0 \\ \Rightarrow \lambda =\frac{-2}{3} \end{gathered}$$
Hence, the yz-plane divides AB in the ratio $-$2 : 3