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  • Explain solution for RD Sharma maths class 12 chapter 28 The Plane exercise 28.6 question 4 sub question 3 maths textbook solution

Explain solution for RD Sharma maths class 12 chapter 28 The Plane exercise 28.6 question 4 sub question 3 maths textbook solution

Answers (1)

Answer:

              \lambda =0

Hint:

              a_{1}a_{2}+b_{1}b_{2}+c_{1}c_{2}=0

Given:

              3x-6y-2z=7 And 2x+y-\lambda=5

Solution:

Here

\begin{aligned} &a_{1}=3, b_{1}=-6, c_{1}=-2, \text { on comparing with } 3 x-6 y-2 z=7\\ &a_{2}=2, b_{1}=1, c_{2}=-\lambda, \text { on comparing with } 2 x+y-\lambda z=5\\ &\text { Since the planes are perpendicular }\\ &\cos \theta=\frac{a_{1} a_{2}+b_{1} b_{2}+c_{1} c_{2}}{\sqrt{a_{1}^{2}+b_{1}^{2}+c_{1}^{2}} \cdot \sqrt{a_{2}^{2}+b_{2}^{2}+c_{2}^{2}}}=0\\ &\therefore a_{1} a_{2}+b_{1} b_{2}+c_{1} c_{2}=0\\ &6-6+2 \lambda=0\\ &\lambda=0 \end{aligned}

 

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