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Question
Given that P(3, 2, –4), Q(5, 4, –6) and R(9, 8, –10) are collinear. Find the ratio in which Qdivides PR.
Solution
Let Q divide PR in the ratio \[\lambda\] Thus, the coordinates of Q are as follows:
\[\left( \frac{9\lambda + 3}{\lambda + 1}, \frac{8\lambda + 2}{\lambda + 1}, \frac{- 10\lambda - 4}{\lambda + 1} \right)\]
But, the coordinates of Q are (5, 4, −6) .
\[\left( \frac{9\lambda + 3}{\lambda + 1}, \frac{8\lambda + 2}{\lambda + 1}, \frac{- 10\lambda - 4}{\lambda + 1} \right)\]
These three equation gives \[\lambda = \frac{1}{2}\] So, Q divides PR in the ratio\[\frac{1}{2}: 1\]
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