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  • Explain solution for RD Sharma maths class 12 chapter 28 The Plane exercise 28.6 question 4 sub question 2 maths textbook solution

Explain solution for RD Sharma maths class 12 chapter 28 The Plane exercise 28.6 question 4 sub question 2 maths textbook solution

Answers (1)

Answer:

              2

Hint:

              \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

Given:

              2x-4y+3z=5\hspace{0.2cm} And \hspace{0.2cm}x+2y+\lambda z=5\\

Solution:

Here

\begin{aligned} &a_{1}=2, b_{1}=-4, c_{1}=3, \text { on comparing with } 2 x-4 y+3 z=5\\ &a_{2}=1, b_{2}=2, c_{2}=\lambda, \text { on comparing with } x+2 y+\lambda z=5\\ &\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, \text { as t } \text { e planes are penpendicular } \cos \left(\frac{\pi}{2}\right)\\ &=0\\ &a_{1} a_{2}+b_{1} b_{2}+c_{1} c_{2}=0\\ &2-8+3 \lambda=0\\ &\lambda=2 \end{aligned}

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