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\[\equiv \left( \frac{3\lambda + 2}{\lambda + 1}, \frac{5\lambda + 4}{\lambda + 1}, \frac{4\lambda + 5}{\lambda + 1} \right)\]

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

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

Hence, the yz-plane divides AB in the ratio 2:3 (externally).