# What is the cross product of [3, 1, -4] and [1, 1, 18] ?

Dec 20, 2015

$\left(22 , - 53 , 2\right)$

#### Explanation:

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

$\left(3 , 1 , - 4\right) \times \left(1 , 1 , 18\right) = | \left(\hat{i} , \hat{j} , \hat{k}\right) , \left(3 , 1 , - 4\right) , \left(1 , 1 , 18\right) |$

$= \hat{i} \left(18 + 4\right) - \hat{j} \left(54 - 1\right) + \hat{k} \left(3 - 1\right)$

$= 22 \hat{i} - 53 \hat{j} + 2 \hat{k}$

$= \left(22 , - 53 , 2\right)$