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  • Explain solution for RD Sharma maths class 12 chapter 26 Direction Cosines and Direction Ratios exercise 26.1 question 13 maths textbook solution

Explain solution for RD Sharma maths class 12 chapter 26 Direction Cosines and Direction Ratios exercise 26.1 question 13 maths textbook solution

Answers (1)

Answer: Angle between lines is \frac{\pi }{2}

Hint: Use dot product formula

Given: \left(a_{1}, b_{1}, c_{1}\right)=(a, b, c) \&\left(a_{2}, b_{2}, c_{2}\right)=(b-c, c-a, a-b). Find angle between two lines.

Solution: we  have \left(a_{1}, b_{1}, c_{1}\right)=(a, b, c) \&\left(a_{2}, b_{2}, c_{2}\right)=(b-c, c-a, a-b)

Now,

            \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}}} \\ &\cos \theta=\frac{(a)(b-c)+(b)(c-a)+(c)(a-b)}{\sqrt{a^{2}+b^{2}+c^{2}} \sqrt{(b-c)^{2}+(c-a)^{2}+(a-b)^{2}}} \\ &\cos \theta=\frac{(a b-a c)+(b c-b a)+(a c-b c)}{\sqrt{a^{2}+b^{2}+c^{2}} \sqrt{(b-c)^{2}+(c-a)^{2}+(a-b)^{2}}} \\ &\cos \theta=0 \\ &\theta=\cos ^{-1}(0) \\ &\theta=\frac{\pi}{2} \end{aligned}

              Therefore, the angle between line is \theta=\frac{\pi}{2}

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