Answer
$4\sqrt 6$
Work Step by Step
The cross product is defined as:
$u \times v=\begin{vmatrix}i&j&k\\m_1&m_2&m_3\\n_1&n_2&n_3\end{vmatrix}=\lt m_2n_3-m_3n_2, m_3n_1-m_1n_3, m_1n_2-m_2b_1 \gt$
The area of parallelogram $A$ is defined as the length of the cross product $u \times v$ .
Now,
$u \times v=\lt (2)(3)-(1)(2),(1)(1)-(3)(3), (3)(2) -(2)(1) \gt=\lt 4,-8,4 \gt$
Then, we have
$A=|u \times v|=\sqrt {(4)^2+(-8)^2+(4)^2}$
or, $A=\sqrt {96}=4\sqrt 6$
