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

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

Answers (1)

Answer:

              \frac{\pi }{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}}}

Given:

            x-y+z=5\hspace{0.2cm} And\hspace{0.2cm} x+2y+z=9

Solution:

Here,

\begin{aligned} &a_{1}=1, b_{1}=-1, c_{1}=1, \text { comparing with } x-y+z=5 \\ &a_{2}=1, b_{2}=2, c_{2}=1, \text { comparing with } x+2 y+z=9 \\ &\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)(1)+(-1)(2)+(1)(1)}{\sqrt{1^{2}+(-1)^{2}+1^{2}} \cdot \sqrt{(1)^{2}+(2)^{2}+(1)^{2}}} \\ &=0 \\ &\theta=\frac{\pi}{2} \end{aligned}

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