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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 27 Straight Line in Space Exercise 27.2 Question 11 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 27 Straight Line in Space  Exercise 27.2 Question 11  Maths Textbook Solution.

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Answer: the angle between the pairs given in the question \cos ^{-1}\frac{2}{3}

Given: find the angle between two lines on of which has direction ratio (2,2,1) while other one is obtained by joining the points (3,1,4) and (7,2,12)

Hint: \begin{aligned} &\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{aligned}

Solution: now \left ( a_{1},b_{1},c_{1}\right )=2,2,1

    While  \begin{aligned} &a_{2}=\left(x_{2}-x_{1}\right)=4 \\ \end{aligned}

             \begin{aligned} &b_{2}=\left(y_{2}-y_{1}\right)=1 \\ &c_{2}=\left(z_{2}-z_{1}\right)=8 \\ \end{aligned}

\begin{aligned} &\cos \theta=\frac{8+2+8}{\sqrt{2^{2}+2^{2}+1^{2} \sqrt{1^{2}+1^{2}+8^{2}}}} \\ \end{aligned}

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

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

 

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