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

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#### Solution

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).*

Concept: Three Dimessional Space

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