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(D) We know the properties of unit vectors in Cartesian coordinates: $\hat{i} 	imes \hat{j} = \hat{k}$,$\hat{j} 	imes \hat{k} = \hat{i}$,and $\hat{k

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$3$

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(D) We know the properties of unit vectors in Cartesian coordinates: $\hat{i} 	imes \hat{j} = \hat{k}$,$\hat{j} 	imes \hat{k} = \hat{i}$,and $\hat{k} 	imes \hat{i} = \hat{j}$.Substituting these into the expression:$\hat{i} \cdot (\hat{j} 	imes \hat{k}) + \hat{j} \cdot (\hat{k} 	imes \hat{i}) + \hat{k} \cdot (\hat{i} 	imes \hat{j}) = \hat{i} \cdot \hat{i} + \hat{j} \cdot \hat{j} + \hat{k} \cdot \hat{k}$.Since the dot product of a unit vector with itself is $1$ (i.e.,$\hat{i} \cdot \hat{i} = 1$,$\hat{j} \cdot \hat{j} = 1$,$\hat{k} \cdot \hat{k} = 1$):$1 + 1 + 1 = 3$.

$\hat{i} \cdot (\hat{j} \times \hat{k}) + \hat{j} \cdot (\hat{k} \times \hat{i}) + \hat{k} \cdot (\hat{i} \times \hat{j}) = $

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