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

1 Answer
Feb 25, 2016

Answer:

(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#