If a cdot hat{i} = a cdot (hat{i} + hat{j}) = | vedclass

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(A) Let the vector $a = x\hat{i} + y\hat{j} + z\hat{k}$.Given $a \cdot \hat{i} = a \cdot (\hat{i} + \hat{j}) = a \cdot (\hat{i} + \hat{j} + \hat{k})$.

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$\hat{i}$

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(A) Let the vector $a = x\hat{i} + y\hat{j} + z\hat{k}$.Given $a \cdot \hat{i} = a \cdot (\hat{i} + \hat{j}) = a \cdot (\hat{i} + \hat{j} + \hat{k})$.From $a \cdot \hat{i} = a \cdot (\hat{i} + \hat{j})$,we get $a \cdot \hat{i} = a \cdot \hat{i} + a \cdot \hat{j}$,which implies $a \cdot \hat{j} = 0$. Thus,$y = 0$.From $a \cdot (\hat{i} + \hat{j}) = a \cdot (\hat{i} + \hat{j} + \hat{k})$,we get $a \cdot \hat{i} + a \cdot \hat{j} = a \cdot \hat{i} + a \cdot \hat{j} + a \cdot \hat{k}$,which implies $a \cdot \hat{k} = 0$. Thus,$z = 0$.Since $a \cdot \hat{i} = x$,and the problem implies $a$ is a unit vector or specific vector satisfying these conditions,if we assume $a = \hat{i}$,then $a \cdot \hat{i} = 1$,$a \cdot (\hat{i} + \hat{j}) = 1$,and $a \cdot (\hat{i} + \hat{j} + \hat{k}) = 1$. Therefore,$a = \hat{i}$ satisfies the given conditions.

If $a \cdot \hat{i} = a \cdot (\hat{i} + \hat{j}) = a \cdot (\hat{i} + \hat{j} + \hat{k})$,then $a$ is equal to

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