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

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

Answers (1)

Answer:

              \cos ^{-1}\left ( -\frac{\sqrt{2}}{3\sqrt{3}} \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:

            x+y-2z=3 And 2x-2y+z=5

Solution:

                  \begin{aligned} &x+y-2 z=3 \\ &a_{1}=1, b_{1}=1, c_{1}=-2 \end{aligned}

\qquad \begin{array}{c} 2 x-2 y+z=5 \\ a_{2}=2, b_{2}=-2, c_{2}=1 \\ \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)(2)+(1)(-2)+(-2)(1)}{\sqrt{(1)^{2}+(1)^{2}+(-2)^{2}} \cdot \sqrt{(2)^{2}+(-2)^{2}+(1)^{2}}} \\ = \frac{-2}{\sqrt{6} \times 3} \\ = \frac{-\sqrt{2}}{3 \sqrt{3}} \\ \theta=\cos ^{-1}\left(-\frac{\sqrt{2}}{3 \sqrt{3}}\right) \end{array}

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