What is the cross product of #[2, 1, -4]# and #[4,3,6] #?
First of all, always remember the the cross product will result in a new vector. So if you get a scalar quantity for your answer, you have done something wrong. The easiest way to compute a three dimensional cross product is the, "cover up method."
Place the two vectors in a 3 x 3 determinant as so:
| i j k |
| 2 1 -4 |
| 4 3 6 |
Next, starting from the left, cover up the left most column, and the top row, so that you are left with:
| 1 -4 |
| 3 6 |
Take the determinant of this to find your i term:
Repeat the procedure covering up the middle column for the j term, and the right column for the k term.
Finally add the three terms together in a pattern of