Answer
${\bf( i-k)}\times{\bf (j+k)}={\bf i-j} +{\bf k}$
Work Step by Step
${\bf (i-k)}\times{\bf v}=\left|\begin{array}{lll}
{\bf i} & {\bf j} & {\bf k}\\
u_{1} & u_{2} & u_{3}\\
v_{1} & v_{2} & v_{3}
\end{array}\right|$
---
${\bf( i-k)}\times{\bf (j+k)}=\left|\begin{array}{rrr}
{\bf i} & {\bf j} & {\bf k}\\
1 & 0 & -1\\
0 & 1 & 1
\end{array}\right|=(0+1){\bf i}-(1-0){\bf j}+(1-0){\bf k}$
$={\bf i-j} +{\bf k}$
