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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 1 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 1 Maths Textbook Solution.

Answers (1)

Answer: the angle between the pairs of lines will be \cos ^{-1}\frac{1}{65}

Given: find the angle between the pairs of lines with direction ratios proportional to

5,-12,13 and -3,4,5

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:

\begin{aligned} &\cos \theta=\frac{-15-48+65}{\sqrt{5^{2}+(-12)^{2}}+13^{2} \sqrt{(-3)^{2}+4^{2}}+5^{2}} \\ &=\frac{-63+65}{\sqrt{338} \sqrt{50}} \\ &=\frac{2}{13 \sqrt{2} \mid 5 \sqrt{2}} \\ &\therefore \quad \cos \theta=\frac{2}{65 \times 2}=\frac{1}{65} \\ &\therefore \quad \theta=\cos ^{-1} \frac{1}{65} \end{aligned}

The angle between the pairs of lines will be \cos ^{-1}\frac{1}{65}

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