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  • Please solve RD Sharma Class 12 Chapter 26 Directions Cosines and Direction Ratio Exercise Multiple Choice Question, question 5 Maths textbook solution.

Please solve RD Sharma Class 12 Chapter 26 Directions Cosines and Direction Ratio Exercise Multiple Choice Question, question 5 Maths textbook solution.

Answers (1)

Answer: (b) Externally in ratio 2:3

Hint: Use section formula

Given: Point(-1,3,4) and (2,-5,6)

To Find: Ratio in which xy plane divide the points

Solution:

 

 

Suppose xy plane divide the line segment joining the points O(-1,3,4) and Q(2,-5,6) in ratio k:1

Using section formula coordinates of the point of intersection are

(x, y, z)=\left(\frac{k(2)+(-1)}{k+1}, \frac{k(-5)+3}{k+1}, \frac{k(6)+4}{k+1}\right)

The z-coordinate of any point of the xy-plane is zero.

\begin{aligned} &\Rightarrow \frac{k(6)+4}{k+1}=0 \\ &\Rightarrow 6 k+4=0 \\ &\Rightarrow k=-\frac{4}{6} \end{aligned}

k:1=-2:3

Therefore, the xy plane divide the given points in 2:3 externally. Hence option(b) externally in the ratio 2:3 is correct.

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