Question

What is the cross product of `[2, 1, -4]` and `[4,3,6]`?

Answer 1

(18,-28,2)

Explanation:

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:

`(1) * (6)-(3)*(-4) = 18`

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 `+, -, +`

This yields:

`18 hat x - 28 hat i + 2 hat j`