  We determine the first non-stable ${\mathbb A}^1$-homotopy sheaf of $SL_n$.
Using techniques of obstruction theory involving the ${\mathbb A}^1$-Postnikov
tower, supported by some ideas from the theory of unimodular rows, we classify
vector bundles of rank $\geq d-1$ on split smooth affine quadrics of dimension
$2d-1$. These computations allow us to answer a question posed by Nori, which
gives a criterion for completability of certain unimodular rows. Furthermore,
we study compatibility of our computations of ${\mathbb A}^1$-homotopy sheaves
with real and complex realization.
