Which of the following is a unit vector?

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(B) unit vector is defined as a vector whose magnitude is equal to $1$.Let us check the magnitude of the given options:For option $A$: $|\hat{i} + \ha

Vedclass · Accepted Answer

$\cos 	heta \hat{i} - \sin 	heta \hat{j}$

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(B) unit vector is defined as a vector whose magnitude is equal to $1$.Let us check the magnitude of the given options:For option $A$: $|\hat{i} + \hat{j}| = \sqrt{1^2 + 1^2} = \sqrt{2} 
eq 1$.For option $B$: $|\cos 	heta \hat{i} - \sin 	heta \hat{j}| = \sqrt{\cos^2 	heta + (-\sin 	heta)^2} = \sqrt{\cos^2 	heta + \sin^2 	heta} = \sqrt{1} = 1$.For option $C$: $|\sin 	heta \hat{i} + 2 \cos 	heta \hat{j}| = \sqrt{\sin^2 	heta + 4 \cos^2 	heta} 
eq 1$.For option $D$: $|\frac{1}{\sqrt{3}}(\hat{i} + \hat{j})| = \frac{1}{\sqrt{3}} \sqrt{1^2 + 1^2} = \frac{\sqrt{2}}{\sqrt{3}} 
eq 1$.Therefore,the vector in option $B$ is a unit vector.

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