Answer
$-\textbf{j}+\textbf{i}$
Work Step by Step
Using the distributive law, we write
$(\textbf{i}+\textbf{j})\times \textbf{k}=(\textbf{i}\times\textbf{k})+(\textbf{j}\times\textbf{k})$
$=-\textbf{j}+\textbf{i}$
(This is because the cross product of any two of the standard base vectors $\textbf{i},\textbf{j}$ and $\textbf{k}$ is equal to the third vector; the product is negative when taken in the opposite order.)
