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  • Need solution for RD Sharma maths class 12 chapter 28 The Plane exercise 28.6 question 3 sub question 2 maths textbook solution

Need solution for RD Sharma maths class 12 chapter 28 The Plane exercise 28.6 question 3 sub question 2 maths textbook solution

Answers (1)

Answer:

              We need to show that the following planes are at right angle

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}}}

Given:

              x=2y+4z=10\hspace{0.2cm} And \hspace{0.2cm}18x+17y+4z=49

Solution:

Here,

\begin{aligned} &a_{1}=1, b_{1}=-2, c_{1}=4, \text { on comparing with } x-2 y+4 z=10\\ &a_{2}=18, b_{2}=17, c_{2}=4, \text { on comparing with } 18 x+17 y+4 z=49\\ &\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}}}\\ &=\frac{1(18)-2(17)+(4)(4)}{\sqrt{(1)^{2}+(-2)^{2}+(4)^{2}} \cdot \sqrt{(18)^{2}+(17)^{2}+(4)^{2}}}\\ &=0\\ &\theta=\frac{\pi}{2} \text {....hence proved } \end{aligned}

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