# What is the cross product of [9,4,-1] and [2, 1, -4] ?

Dec 21, 2015

$\left(- 15 , 34 , 1\right)$

#### Explanation:

The cross product of two 3-dimesnional vectors in ${\mathbb{R}}^{3}$ may be given as a matrix determinant

$\left(9 , 4 , - 1\right) \times \left(2 , 1 , - 4\right) = | \left(\hat{i} , \hat{j} , \hat{k}\right) , \left(9 , 4 , - 1\right) , \left(2 , 1 , - 4\right) |$

$\hat{i} \left(- 16 + 1\right) - \hat{j} \left(- 36 + 2\right) + \hat{k} \left(9 - 8\right)$

$= - 15 \hat{i} + 34 \hat{j} + \hat{k}$

$= \left(- 15 , 34 , 1\right)$