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  • Need solution for RD Sharma maths class 12 chapter 28 The Plane exercise 28.6 question 2 sub question 1 maths textbook solution

Need solution for RD Sharma maths class 12 chapter 28 The Plane exercise 28.6 question 2 sub question 1 maths textbook solution

Answers (1)

Answer:

              \frac{\pi }{3}

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:

              2 x-y+z=4 \text { and } x+y+2 z=3

Solution:

\begin{aligned} &2 x-y+z=4 \\ &a_{1}=2, b_{1}=-1, c_{1}=1 \\ &x+y+2 z=3 \\ &a_{2}=1, b_{2}=1, c_{2}=2 \\ &\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(1)+(-1)(1)+(1)(2)}{\sqrt{4+1+1} \cdot \sqrt{1+1+4}} \\ &=\frac{3}{\sqrt{6} \cdot \sqrt{6}}=\frac{1}{2} \\ & \end{aligned}

\theta=\frac{\pi}{3}

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