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  • Explain solution for RD Sharma maths class 12 chapter 26 Direction Cosines and Direction Ratios exercise 26.1 question 8 maths textbook solution

Explain solution for RD Sharma maths class 12 chapter 26 Direction Cosines and Direction Ratios exercise 26.1 question 8 maths textbook solution

Answers (1)

Answer: Angle between two vectors is \cos ^{-1}\left(\frac{20}{21}\right)

Hint: Use dot product formula.

Given: \left(a_{1}, b_{1}, c_{1}\right)=(2,3,6) \&\left(a_{2}, b_{2}, c_{2}\right)=(1,2,2). Find angle between two lines

Solution: here we have  \left(a_{1}, b_{1}, c_{1}\right)=(2,3,6) \&\left(a_{2}, b_{2}, c_{2}\right)=(1,2,2)

Let \theta be the angle between two lines whose direction ratios are \left(a_{1}, b_{1}, c_{1}\right)  &  \left(a_{2}, b_{2}, c_{2}\right)

              \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{(2)(1)+(3)(2)+(6)(2)}{\sqrt{2^{2}+(3)^{2}+(6)^{2}} \sqrt{1^{2}+(2)^{2}+2^{2}}} \\ &\cos \theta=\frac{2+6+12}{\sqrt{49} \sqrt{9}} \\ &\cos \theta=\frac{20}{21} \\ &\theta=\cos ^{-1}\left(\frac{20}{21}\right) \end{aligned}

Therefore the angle between lines is \cos ^{-1}\left(\frac{20}{21}\right)                                        

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