Question:
Find the cross product: <3, 2, 1> x <1, 2, 3>

Answer:
| i  j  k |
| 3  2  1 | = < |2 1|    |3 1|  |3 2| > = < 6-2, -(9-1), 6-2> = <4, -8, 4>
| 1  2  3 |     |2 3|,  -|1 3|, |1 2|

Check
<4, -8, 4> dot <3, 2, 1> = 12 - 16 + 4 = 0  yes!
<4, -8, 4> dot <1, 2, 3> = 4 - 16 + 12 = 0  yes!