The value of $a$ for which the volume of the parallelopiped formed by vectors $\hat i+a\hat j+\hat k,\:\:\hat j+a\hat k\:\:and\:\: a\hat i+\hat k$ becomes minimum is ?

Question

$\begin{array}{1 1} \frac{1}{\sqrt 3} \\ \frac{1}{\sqrt 3} \\ \sqrt 3 \\ - \sqrt 3 \end{array}$