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