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

Nov 13, 2016

The answer is 〈3,1,-5〉

#### Explanation:

Let vecu=〈1,2,1〉

and vecv=〈2,-1,1〉

The cross product is given by the determinant

 ∣ ((veci,vecj,veck) , (1,2,1) , (2,-1,1)) ∣

$= \vec{i} \left(2 + 1\right) - \vec{j} \left(1 - 2\right) + \vec{k} \left(- 1 - 4\right)$

$= 3 \vec{i} + \vec{j} - 5 \vec{k}$

vecw=〈3,1,-5〉

Verifications, by doing the dot product

vecw.vecu=〈3,1,-5〉.〈1,2,1〉=3+2-5=0

vecw.vecv〈3,1,-5〉.〈2,-1,1〉=6-1-5=0

So, $\vec{w}$ is perpendicular to $\vec{u}$ and $\vec{v}$