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  • Provide Solution For R.D. Sharma Maths Class 12 Chapter 22 Algebra of Vectors Exercise Very Short Answer Type Question 17 Maths Textbook Solution.

Provide Solution For  R.D. Sharma Maths Class 12 Chapter 22 Algebra of Vectors  Exercise Very Short Answer Type  Question 17 Maths Textbook Solution.

Answers (1)

Answer: \frac{1}{\sqrt{3}} \hat{i}+\frac{1}{\sqrt{3}} \hat{j}+\frac{1}{\sqrt{3}} \hat{k}

Hint: You must know the rules of vector functions

Given: Write a unit vector making equal acute angles with the coordinate axes

Solution: Suppose \vec{r} makes an angle \alpha with each of the axes OX, OY and OZ

Then its direction cosines are l=\cos \alpha, m=\cos \alpha, n=\cos \alpha

            Now,

                    \begin{aligned} &l^{2}+m^{2}+n^{2}=1 \\ &\Rightarrow l^{2}+l^{2}+l^{2}=1 \; \; \; \; \; \; \; \; \; \; \; \; \quad[l=m=n] \\ &\Rightarrow 3 l^{2}=1 \\ &\Rightarrow l^{2}=\frac{1}{3} \\ &\Rightarrow l=\pm \frac{1}{\sqrt{3}} \end{aligned}

Since, we know angle is acute, Hence we only take positive values

            ∴ Unit vector is \frac{1}{\sqrt{3}} \hat{i}+\frac{1}{\sqrt{3}} \hat{j}+\frac{1}{\sqrt{3}} \hat{k}

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