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  • Given that P (3, 2, – 4), Q (5, 4, – 6) and R (9, 8, –10) are collinear. Find the ratio in which Q divides PR.

2   Given that P (3, 2, – 4), Q (5, 4, – 6) and R (9, 8, –10) are collinear. Find the ratio in which Q divides PR.

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best_answer

Given Three points,

P (3, 2, – 4), Q (5, 4, – 6) and R (9, 8, –10)

Let point Q divides PR internally in the ratio \lambda:1

Now,

According to the section formula , The point Q in terms of P,Q and \lambda is:

\left ( \frac{9\lambda+3}{\lambda+1},\frac{8\lambda+2 }{\lambda +1},\frac{-10\lambda-4}{\lambda+1}\right )=(5,4,-6)

\frac{9\lambda+3}{\lambda+1}=5

{9\lambda+3}}=5(\lambda+1)

4\lambda =2

\lambda =\frac{1}{2}

Hence, point Q divides PR in the ratio of 1:2.

 

Posted by

Pankaj Sanodiya

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