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  • Need solution for RD Sharma maths class 12 chapter 28 The Plane exercise 28.6 question 2 sub question 5 maths textbook solution

Need solution for RD Sharma maths class 12 chapter 28 The Plane exercise 28.6 question 2 sub question 5 maths textbook solution

Answers (1)

Answer:

              \cos ^{-1}\left ( \frac{4}{21} \right )

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:

              2x+y+2z=5 And 3x-6y-2z

Solution:

Here,

\begin{aligned} &a_{1}=2, b_{1}=1, c_{1}=-2, \text { on comparing with } 2 x+y-2 z=5 \\ &a_{2}=3, b_{2}=-6, c_{2}=-2, \text { on comparing with } 3 x-6 y-2 z=7 \\ &\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{(2)(3)+(1)(-6)+(-2)(-2)}{\sqrt{(2)^{2}+(1)^{2}+(-2)^{2}} \cdot \sqrt{(3)^{2}+(-6)^{2}+(-2)^{2}}} \\ &=\frac{4}{3 \times 7}=\frac{4}{21} \\ &\theta=\cos ^{-1}\left(\frac{4}{21}\right) \end{aligned}

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