random matrices - Probability on the distance

Let $A$ be an $ntimes n$ gaussian matrix whose entries are i.i.d.
copies of a gaussian variable, and $left{ a_{j}right} _{j=1}^{n}$
be the column vectors of $A$. How to show that the probability
$mathbb{P}left(dgeq tright)leq Ce^{-ct}$
for some $c,C>0$ and every $t>0$, where $d$ is the distance between
$a_{1}$ and the $n-1$-dimensional subspace spanned by $a_{2},cdots,a_{n}$.

Thanks a lot!