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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 4 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 4 Maths Textbook Solution.

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

Given: find the angle between the pairs of lines with direction ratio proportional to(a,b,c)and

(b-c), (c-a) (a-b)

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} & a_{1} a_{2}+b_{1} b_{2}+c_{1} c_{2}=a b-a c+b c-b a+a c-b c=0 \\ \end{aligned}

               \begin{aligned} & \therefore \cos \theta=\frac{0}{\sqrt{a^{2}+b^{2}+c^{2}} \sqrt{(b-c)^{2}+(c-a)^{2}+(a-b)^{2}}} \\ \end{aligned}

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

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

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

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

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