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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 22 Algebra of Vectors Exercise very Short Answer type Question 47 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 22 Algebra of Vectors  Exercise very Short Answer type Question 47 Maths Textbook Solution.

Answers (1)

Answer: \vec{a}=5\left ( \hat{i}+0\hat{j}+\hat{k} \right )

Hint: You must know the rules of vector functions

Given: Find a vector \vec{a} of magnitude -5\sqrt{2} ,making angle\frac{\pi }{4} with x- axis,\frac{\pi }{2} with y-axis and \thetawith z-axis

Solution: \frac{\pi }{4} with x- axis, \frac{\pi }{2} with y-axis and \theta with z-axis

\begin{aligned} &l=\cos \frac{\pi}{4}=\frac{1}{\sqrt{2}} \\ &m=\cos \frac{\pi}{2}=0 \\ &n=\cos \theta \\ &\therefore l^{2}+m^{2}+n^{2}=1 \\ &\frac{1}{2}+0+\cos ^{2} \theta=1 \\ &\frac{1}{2}=1-\cos ^{2} \theta \\ &\cos ^{2} \theta=1-\frac{1}{2} \\ &\cos ^{2} \theta=\frac{1}{2} \\ &\cos \theta=\frac{1}{\sqrt{2}} \\ \end{aligned}Since \theta is  an acute angle

Now,

\begin{aligned} &\vec{a}=|\vec{a}|(l \hat{i}+m \hat{j}+n \hat{k}) \\ &\vec{a}=5 \sqrt{2}\left(\frac{1}{\sqrt{2}} \hat{i}+0 \hat{j}+\frac{1}{\sqrt{2}} \hat{k}\right) \\ &\vec{a}=5(\hat{i}+0 \hat{j}+\hat{k}) \end{aligned}

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