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  • Provide Solution For R.D.Sharma Maths Class 12 Chapter 27 Straight Line in Space Exercise 27.2 Question 9 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 9 Sub Question 2 Maths Textbook Solution.

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Answer: the angle between the given pairs of a line is \cos ^{-1}=\frac{10}{9\sqrt{22}}

Given: find the angle between the pairs of lines

\begin{gathered} \frac{x-1}{2}=\frac{y-1}{3}=\frac{z-3}{-3} \text { and } \frac{x+3}{-1}=\frac{y-5}{8}=\frac{z-1}{4} \\ \end{gathered}

Hint:\begin{gathered} \cos \theta=\frac{\vec{a} \cdot \vec{b}}{|\vec{a}||\vec{b}|} \end{gathered}

Solution: Direction \: ratio \: of line_{1}=2,3,-3

         Direction \; vector \vec{a}=2 \hat{i}+3 \hat{j}-3 \hat{k}\\\\

        Direction ratio of line _{2}=-1,8,4\\\\\

        Direction \: vector \vec{b}=-\hat{i}+8 \hat{j}+4 \hat{k}

\begin{aligned} \cos \theta &=\frac{-2+24-12}{\left|\sqrt{2^{2}+3^{2}-(3)^{2}} \| \sqrt{(-1)^{2}+8^{2}+4^{2}}\right|} \\ &=\frac{24-14}{|\sqrt{22} \| \sqrt{81}|} \\ &=\frac{10}{9 \sqrt{22}} \\ & \theta=\cos ^{-1}=\frac{10}{9 \sqrt{22}} \end{aligned}

The angle between the points will be \cos ^{-1}=\frac{10}{9\sqrt{22}}

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