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  • Provide solution for RD Sharma maths class 12 chapter 26 Direction Cosines and Direction Ratios exercise Fill in the blanks question 18

Provide solution for RD Sharma maths class 12 chapter 26 Direction Cosines and Direction Ratios exercise Fill in the blanks question 18

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Final Answer  →-\frac{3}{7}
Hint :

In zx plane y-coordinate is zero and y coordinate of points divide line segment.
Given :  

Points are (2,3,1) \text { and }(6,7,1)
To find:

 Ratio in which line is divided
Solution :

Let zx-plane  divide the line segment in ratio

                                \left(m_{1}\right) \quad\quad\quad\quad\left(m_{2}\right)

                                p\quad \quad\quad\quad\quad\quad\quad1

            (2,3,1)\quad\quad\quad\quad (x, 0, z)\quad\quad\quad\quad (6,7,1)

        \left(x_{1}, y_{1}, z_{1}\right) \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\left(x_{2}, y_{2}, z_{2}\right)

                                            \text { zx plane }

Using section formula,

\begin{aligned} &y=\frac{m_{1} y_{2}+m_{2} y_{2}}{m_{1}+m_{2}} \\\\ &0=\frac{7 p+3}{p+1} \end{aligned}

\begin{aligned} &7 p+3=0 \\\\ &p=\frac{-3}{7} \end{aligned}

Therefore, the zx plane divide the line in ratio \frac{-3}{7}

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