A vector of magnitude $4$ which is equally inclined to the vectors $\hat{i} + \hat{j}$, $\hat{j} + \hat{k}$, and $\hat{k} + \hat{i}$, is:

Question

$\frac{4}{\sqrt{3}}(\hat{i} - \hat{j} - \hat{k})$

$\frac{4}{\sqrt{3}}(\hat{i} + \hat{j} - \hat{k})$

$\frac{4}{\sqrt{3}}(\hat{i} + \hat{j} + \hat{k})$

none of these

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