Answer
$-i+j+5k.$
Work Step by Step
We know that a vector will be orthogonal to two vectors if and only if it is their cross-product (multiplied by any constant).
We know that for a matrix
\[
\left[\begin{array}{rrr}
a & b & c \\
d &e & f \\
g &h & i \\
\end{array} \right]
\]
the determinant, $D=a(ei-fh)-b(di-fg)+c(dh-eg).$
We know that if we have two vectors $v=ai+bj+ck$ and $w=di+ej+fk$, then $v\times w$ can be obtained by the determinant of: \[
\left[\begin{array}{rrr}
i & j & k \\
a &b & c \\
d &e & f \\
\end{array} \right]
\]
Hence here $D=u\times (i+j)=i((-3)\cdot0-1\cdot1)-j(2\cdot0-1\cdot1)+k(2\cdot1-(-3)\cdot1)=-i+j+5k.$
