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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 22 Algebra of Vectors Exercise 22.9 Question 6 Sub Question 2 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 22 Algebra of Vectors  Exercise 22.9 Question 6 Sub Question 2 Maths Textbook Solution.

Answers (1)

Answer:\frac{6}{7},\frac{-2}{7},\frac{-3}{7}

Given: 6\hat{i}-2\hat{j}-3\hat{k}

Hint: Find \cos \alpha ,\cos \beta ,\cos \gamma

Explanation: Let \mu =6\hat{i}-2\hat{j}-3\hat{k}  be the given vector.

Then magnitude of vector ‘\mu ’ is |\vec{\mu}|=\sqrt{6^{2}+(-2)^{2}+(-3)^{2}}=\sqrt{49}=7

Let the direction cosines of vector are \cos \alpha ,\cos \beta ,\cos \gamma

We have \begin{aligned} &\cos \alpha=\frac{\mu i}{|\vec{\mu}|}=\frac{6}{7} \\ \end{aligned}

We have \begin{aligned} &\cos \beta=\frac{\mu \cdot j}{|\vec{\mu}|}=\frac{-2}{7} \\ \end{aligned}

We have \begin{aligned} &\cos \gamma=\frac{\mu-k}{|\vec{\mu}|}=\frac{-3}{7} \end{aligned}

\therefore The direction cosines of given vector are \frac{6}{7},\frac{-2}{7},\frac{-3}{7}

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