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  • Explain solution for RD Sharma maths class 12 chapter 26 Direction Cosines and Direction Ratios exercise 26.1 question 6 maths textbook solution

Explain solution for RD Sharma maths class 12 chapter 26 Direction Cosines and Direction Ratios exercise 26.1 question 6 maths textbook solution

Answers (1)

Answer: Angle between two vectors is \frac{\pi }{2}

Hint: Use dot product formula

Given: \left ( a_{1},b_{1},c_{1} \right )=\left ( 1,-2,1 \right )and \left ( a_{2},b_{2},c_{2} \right )=\left ( 4,3,2 \right ). Find angle between two vectors.

Solution:

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

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{(1)(4)+(-2)(3)+(1)(2)}{\sqrt{1^{2}+(-2)^{2}+(1)^{2}} \sqrt{4^{2}+3^{2}+2^{2}}} \\ &\cos \theta=\frac{4-6+2}{\sqrt{6} \sqrt{29}} \\ &\cos \theta=0 \\ &\theta=\cos ^{-1}(0)=\frac{\pi}{2} \end{aligned}

        Therefore, angle between two vectors is \frac{\pi}{2}

 

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