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  • Please solve RD Sharma Class 12 Chapter 26 Directions Cosines and Direction Ratio Exercise Multiple Choice Question, question 9  Maths textbook solution.

Please solve RD Sharma Class 12 Chapter 26 Directions Cosines and Direction Ratio Exercise Multiple Choice Question, question 9  Maths textbook solution.

Answers (1)

Final Answer: (a) 3:2 externally

Hint: Use section formula

Given: Points P(3,2,-4), Q(5,4,-6) and R(9,8,-10)

To Find: R divides PQ in what ratio

Solution:

Let R divides the line PQ in the ratio k:1

Using section formula

\begin{aligned} &(x, y, z)=\left[\Rightarrow \frac{k\left(x_{2}\right)+x_{1}}{k+1}, \frac{k\left(y_{2}\right)+y_{1}}{k+1}, \frac{k\left(z_{2}\right)+z_{1}}{k+1}\right] \\ &(9,8,-10)=\left[\frac{k(5)+3}{k+1}, \frac{k(4)+2}{k+1}, \frac{k(-6)+(-4)}{k+1}\right] \\ &(9,8,-10)=\left[\frac{5 k+3}{k+1}, \frac{4 k+2}{k+1}, \frac{-6 k-4}{k+1}\right] \end{aligned}

comparing x-coordinate

\begin{aligned} &9=\frac{5 k+3}{k+1} \\ &9(k+1)=5 k+3 \\ &4 k=-6 \\ &k=\frac{-3}{2} \end{aligned}

Therefore R divides the line PQ in ratio 3:2 externally. Hence option (b) is correct.

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