Answer
If the magnitude of $a$ (that is, $|a|$) and the magnitude of $b$ (that is, $|b|$) is known and the angle between $a$ and $b$ (that is, $\theta$) is known, the product of the magnitudes and the sine of the angle is the cross product of $a$ and $b$.
$a \times b= |a| |b| sin \theta$
The direction will be perpendicular to both $a$ and $b$.
This implies that
$a \times b=\lt a_2b_3-a_3b_2,a_3b_1-a_1b_3,a_1b_2-a_2b_1 \gt$
Work Step by Step
If the magnitude of $a$ (that is, $|a|$) and the magnitude of $b$ (that is, $|b|$) is known and the angle between $a$ and $b$ (that is, $\theta$) is known, the product of the magnitudes and the sine of the angle is the cross product of $a$ and $b$.
$a \times b= |a| |b| sin \theta$
The direction will be perpendicular to both $a$ and $b$.
This implies that
$a \times b=\lt a_2b_3-a_3b_2,a_3b_1-a_1b_3,a_1b_2-a_2b_1 \gt$
