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प्रश्न
The ratio in which the line joining (2, 4, 5) and (3, 5, –9) is divided by the yz-plane is
विकल्प
2 : 3
3 : 2
–2 : 3
4 : –3
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उत्तर
\[-\]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
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