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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 3 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 3 Maths Textbook Solution.

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Answer: the angle between the given points of lines will be 90^{0}

Given: find the angle between the pairs of lines with direction ratio proportional to (1,2,-2) and

(-2,2,1)

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{-2+4-2}{\sqrt{1^{2}+2^{2}+(-2)^{2}} \sqrt{(-2)^{2}+2^{2}+1^{2}}} \\ \end{aligned}

                                       \begin{aligned} &=\frac{0}{\sqrt{1+4+4} \sqrt{4+4+1}} \\ \end{aligned}

                            \begin{aligned} &\cos \theta=0 \\ \end{aligned}

                       \begin{aligned} \cos \theta=90^{\circ} \\ \therefore \theta=90^{\circ} \end{aligned}

The angle between the pairs of lines will be \theta =90^{0}                                                                                                                                                                                                                                                                                                                                                                                                            

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