The largest value of a, for which the perpendicuar distance of the plane containing the lines \(...

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The largest value of a, for which the perpendicuar distance of the plane containing the lines \( r=(\hat{i}+\hat{j})+\lambda(\hat{i}+a \hat{j}-\hat{k}) \) and \( r=(\hat{i}+\hat{j})+\mu(-\hat{i}+\hat{j}-a \hat{k}) \) from the point \( (2,1,4) \) is \( \sqrt{3} \), is
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