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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 28 The Plane Exercise 28.13 Question 15 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 28 The Plane Exercise 28.13 Question 15 Maths Textbook Solution.

Answers (1)

Answer: I^{2}+m^{2}=2

Hint: use simultaneous equation to solve

Given:  \frac{x-3}{2}=\frac{y+2}{-1}=\frac{z+4}{3}

Solution: we know that the lines

            \begin{aligned} &\frac{x-x_{1}}{l_{1}}=\frac{y-y_{1}}{m_{1}}=\frac{z-z_{1}}{n_{1}} \text { lies in plane } a_{1}+b y+c z+d=0 \text { then }\\ &a_{1} \lambda_{1}+b y_{1}+c z_{1}+d=0 \text { and } a l+b m+c n=0 \text { here, }\\ &\lambda_{1}=3, y_{1}=-2, z_{1}=-4 \text { and } l=2, m=-1, n=3 \end{aligned}

           and

             \begin{aligned} &2 l-m-3=0 \\ &3 l-2 m=5 \\ &3 l-2 m=5------(1) \\ &2 l-m=3------(2) \end{aligned}

Multiply equation (1) by 2 and equation (2) by 3 and then subtract we get

                m=-1

                l=1

                l^{2}+m^{2}=2

 

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