# What is the cross product of [2, 6, -1] and [1, 1, 18] ?

Nov 6, 2016

The cross product is 〈109,-37,-4〉

#### Explanation:

The cross product of the 2 vectors is given by the determinant

∣((veci,vecj,veck),(2,6,-1),(1,1,18))∣

$= \vec{i} \left(108 + 1\right) - \vec{j} \left(36 + 1\right) + \vec{k} \left(2 - 6\right)$

$109 \vec{i} - 37 \vec{j} - 4 \vec{k}$
So the cross product is 〈109,-37,-4〉

Verifications, the dots products must $= 0$

So, 〈109,-37,-4〉.〈2,6,-1〉=218-222+4=0

〈109,-37,-4〉.〈1,1,18〉=109-37-72=0
So the cross product is perpendicular to the two vectors