Is it possible to find the unitary matrix in the following case?

Question

I have a unitary matrix $\mathbb{U}$ given as follows $$\mathbb{U}=[\mathbb{a}~\mathbb{b}_1~\mathbb{b}_2~\cdots\mathbb{b}_{N-1}]$$ where $\mathbb{a,~b_1~\cdots b}_{N-1}$ are the complex column vectors with $N$ elements each. I only know the elements of $\mathbb{a}$ so is it possible to construct $\mathbb{U}$ with only $\mathbb{a}$ known. Any help in this regard will be much appreciated. Thanks in advance.