Question

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

Options

•  2 : 3

• 3 : 2

• –2 : 3

• 4 : –3 

Answer 1

 \[-\]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.

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

\[ \Rightarrow 3\lambda + 2 = 0\]

\[ \Rightarrow \lambda = \frac{- 2}{3}\]

Hence, the yz-plane divides AB in the ratio \[-\] 2 : 3