Answer
See the explanation below.
Work Step by Step
The two vectors in component form can be expressed as:
$u =\lt u_{1}, u_{2}, u_{3}\gt $ and $v =\lt v_{1}, v_{2}, v_{3}\gt $
or, $u =u_{1} i+u_{2}j+ u_{3}k$ and $v =v_{1} i+v_{2} j+v_{3} k$
Their vector cross product can be determined as:
$u \times v=\begin{vmatrix}i &j&k\\u_1&u_2& u_3 \\v_1&v_2&v_3\end{vmatrix}=i\begin{vmatrix} u_2& u_3 \\v_2&v_3\end{vmatrix}-j \begin{vmatrix}i & k\\u_1& u_3 \\v_1&v_3\end{vmatrix}+k \begin{vmatrix} u_1&u_2 \\v_1&v_2 \end{vmatrix}$
