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  • Provide Solution For R.D. Sharma Maths Class 12 Chapter 22 Algebra of Vectors Exercise 22.9 Question 6 Sub Questions 1 Maths Textbook Solution.

Provide Solution For R.D. Sharma Maths Class 12 Chapter 22 Algebra of Vectors  Exercise 22.9 Question 6  Sub Questions 1 Maths Textbook Solution.

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Answer:\frac{2}{3},\frac{2}{3},\frac{-1}{3}

Given: 2\hat{i}+2\hat{j}-\hat{k}

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

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

Then magnitude of vector '\mu ' is |\vec{u}|=\sqrt{2^{2}+2^{2}+(-1)^{2}}=\sqrt{9}=3

Let the direction cosines of vector ‘u’ be \cos \alpha ,\cos \beta ,\cos \gamma

We have \begin{aligned} &\cos \alpha=\frac{\mu i}{|\vec{\mu}|}=\frac{2}{3} \\ \end{aligned}

We have \begin{aligned} &\cos \beta=\frac{\mu \cdot j}{|\vec{\mu}|}=\frac{2}{3} \\ \end{aligned}

We have \begin{aligned} &\cos \gamma=\frac{\mu \cdot k}{|\vec{\mu}|}=\frac{-1}{3} \end{aligned}

\therefore The direction cosines of given vector are\frac{2}{3},\frac{2}{3},\frac{-1}{3}

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