A unit vector perpendicular to both $\hat{i} + \hat{j}$ and $\hat{j} + \hat{k}$ is
$\hat{i} - \hat{j} + \hat{k}$
$\hat{i} + \hat{j} + \hat{k}$
$\frac{\hat{i} - \hat{j} + \hat{k}}{\sqrt{3}}$
$\frac{\hat{i} + \hat{j} + \hat{k}}{\sqrt{3}}$
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