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  • Please solve RD Sharma class 12 chapter 23 Scaler and Dot Product exercise Multiple choice question 5 maths textbook solution

Please solve RD Sharma class 12 chapter 23 Scaler and Dot Product exercise Multiple choice question 5 maths textbook solution

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Answer: Option (b) unit vector

Hint: The formula of Magnitude of a vector=\sqrt{a^{2}+b^{2}+c^{2}}

Given:

\operatorname{Vector}(\cos \alpha \cos \beta) \hat{\imath}+(\cos \alpha \sin \beta) \hat{\jmath}+(\sin \alpha) \hat{k}

Solution: (\cos \alpha \cos \beta) \hat{\imath}+(\cos \alpha \sin \beta) \hat{\jmath}+(\sin \alpha) \hat{k}

Magnitude of a vector =\sqrt{a^{2}+b^{2}+c^{2}}

Magnitude of a vector=\sqrt{\left(\cos ^{2} \alpha \cos ^{2} \beta\right)+\left(\cos ^{2} \alpha \sin ^{2} \beta\right)+\left(\sin ^{2} \alpha\right)}

                                =\sqrt{\cos ^{2} \alpha\left(\cos ^{2} \beta+\sin ^{2} \beta\right)+\sin ^{2} \alpha} \quad\left[\because \cos ^{2} x+\sin ^{2} x=1\right]

                                \begin{aligned} &=\sqrt{\cos ^{2} \alpha+\sin ^{2} \alpha} \\ &=\sqrt{1} \\ &=1 \end{aligned}

Hence, it is unit vector

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