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  • Explain Solution R.D.Sharma Class 12 Chapter 22 Algebra of Vectors Exercise Very Short Answer Type Question 28 Maths Textbook Solution.

Explain Solution R.D.Sharma Class 12 Chapter 22 Algebra of Vectors  Exercise Very Short Answer Type Question 28 Maths Textbook Solution.

Answers (1)

Answer: \theta =30^{o}

Hint: You must know the rules of vector functions

Given: A unit vector \vec{r}make angles \frac{\pi }{3},\frac{\pi }{2} with \hat{j} &\hat{k} and an acute angle \theta with \hat{i}.find \theta

Solution: Angle \frac{\pi }{3},\frac{\pi }{2} with \hat{j} &\hat{k}

   Let l , m , n be the direction cosines

\begin{aligned} &l=\cos \theta, m=\cos \frac{\pi}{3}, n=\cos \frac{\pi}{2} \\ &l=\cos \theta, m=\frac{1}{2}, n=0 \\ \end{aligned}

Now,\begin{aligned} &l^{2}+m^{2}+n^{2}=1 \\ \end{aligned}

\begin{aligned} &l^{2}+\frac{1}{4}+0=1 \\ &l^{2}=\frac{3}{4} \\ &l=\pm \sqrt{\frac{3}{4}} \Rightarrow \pm \frac{\sqrt{3}}{2} \\ \end{aligned}

But we know angle made with \hat{i}is an acute angle so, we use the positive value.

\therefore \theta =30^{o}                                                                \left [ \therefore \cos ^{-1}\left ( \frac{\sqrt{3}}{2} \right )=30^{0} \right ]

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