The value of $\alpha$, so that the volume of the parallelopiped formed by $\hat{i}+\alpha\hat{j}+\hat{k}$, $\hat{j}+\alpha\hat{k}$ and $\alpha\hat{i}+\hat{k}$ becomes maximum, is
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Logic Tip: When looking for a maximum, the second derivative must be negative (concave down). By simply looking at the second derivative $V''(\alpha) = 6\alpha$, it is immediately obvious that we need the negative root of $\alpha$ to satisfy $6\alpha<0$.