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  • Explain Solution R.D.Sharma Class 12 Chapter 22 Algebra of Vectors Exercise 22.9 Question 6 Sub Question 3 Maths Textbook Solution.

Explain Solution R.D.Sharma Class 12 Chapter 22 Algebra of Vectors  Exercise 22.9 Question 6 Sub Question 3 Maths Textbook Solution.

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Answer:\frac{3}{5},0,\frac{-4}{5}

Given: 3\hat{i}-4\hat{k}

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

Explanation: Let \mu =3\hat{i}+o\hat{j}-4\hat{k}be the given vector.

Then magnitude of vector '\mu ' is |\vec{\mu}|=\sqrt{3^{2}+0^{2}+(-4)^{2}}=\sqrt{25}=5

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{3}{5} \\ \end{aligned}

We have \begin{aligned} &\cos \beta=\frac{\mu \cdot j}{|\vec{\mu}|}=\frac{0}{5} \\ \end{aligned}

We have \begin{aligned} &\cos \gamma=\frac{\mu \cdot k}{|\vec{\mu}|}=\frac{-4}{5} \end{aligned}

\therefore The direction cosines of given vector are\frac{3}{5},0,\frac{-4}{5}

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