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  • Provide Solution For R.D.Sharma Maths Class 12 Chapter 27 Straight Line in Space Exercise 27.2 Question 10 Sub Question 2 Maths Textbook Solution.

Provide Solution For R.D.Sharma Maths Class 12 Chapter 27 Straight Line in Space Exercise 27.2 Question 10 Sub Question 2 Maths Textbook Solution.

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Answer: the angle between the given pairs of lines will be \cos ^{-1}\frac{2}{3}

Given: find the angle between the pairs of lines with direction ratios proportion to2,2,1 and 4,1,8

Hint:\begin{gathered} \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} \sqrt{a_{2}^{2}+b_{2}^{2}+c_{2}^{2}}}} \\ \end{gathered}

Solution:\begin{gathered} \cos \theta=\frac{8+2+8}{\sqrt{2^{2}+2^{2}+1^{2}} \sqrt{4^{2}+1^{2}+8^{2}}} \\ \end{gathered}

                                                       \begin{gathered} =\frac{18}{\sqrt{9} \sqrt{81}} \\ =\cos \theta=\frac{2}{3} \\ \therefore \theta=\cos ^{-1} \frac{2}{3} \end{gathered}

So the angle between the pairs of lines will be \cos ^{-1}\frac{2}{3}

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