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  • Need solution for RD Sharma maths class 12 chapter 22 Algebra of Vectors exercise Multiple choice question 7

Need solution for RD Sharma maths class 12 chapter 22 Algebra of Vectors exercise Multiple choice question 7

Answers (1)

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Answer: Unit vector

Hint: \hat{k} is which vector

Given: The vector \cos \alpha \cos \beta \hat{i}+\cos \alpha \sin \beta \hat{i}+\sin \alpha \hat{k}

Solution:

\begin{aligned} &|\vec{A}|=\sqrt{(\cos \alpha \cos \beta)^{2}+(\cos \alpha \sin \beta)^{2}+\sin ^{2} \alpha} \\\\ &=\sqrt{\cos ^{2} \alpha\left(\cos ^{2} \beta+\sin ^{2} \beta\right)+\sin ^{2} \alpha}\\\\ &=\sqrt{\cos ^{2} \alpha+\sin ^{2} \alpha}=1 \text { (Unit vector) } \end{aligned}\quad\left(\cos ^{2} \beta+\sin ^{2} \beta=1\right)

 

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