# What is the cross product of [3, 0, 5] and [3,-6,4] ?

Feb 19, 2016

$\left[3 , 0 , 5\right] \times \left[3 , - 6 , 4\right] = \left[30 , 3 , - 18\right]$

#### Explanation:

[i j k]
[3 0 5]
[3 -6 4]

To calculate the cross product, cover set the vectors out in a table as shown above. Then cover up the column for which you're calculating the value of (e.g. if looking for the i value cover the first column). Next take the product on the top value in the next column to the right and the bottom value of the remaining column. Subtract from this the product of the two remaining values. This has been carried out below, to show how it's done:

i = (04) - (5(-6)) = 0 - (-30) = 30
j = (53) - (34) = 15 - 12 = 3
k = (3(-6)) - (03) = -18 - 0 = -18

Therefore:
$\left[3 , 0 , 5\right] \times \left[3 , - 6 , 4\right] = \left[30 , 3 , - 18\right]$