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

Feb 25, 2016

(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:

$\left(1\right) \cdot \left(6\right) - \left(3\right) \cdot \left(- 4\right) = 18$

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:

$18 \hat{x} - 28 \hat{i} + 2 \hat{j}$