What is the cross product of $[-1,0,1]$ and $[0,1,2]$ ?

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Answer 1 · 2017-01-17T13:05:57

The cross product is $=〈-1,2,-1〉$

The cross product is calculated with the determinant

$| (veci,vecj,veck), (d,e,f), (g,h,i) |$

where $〈d,e,f〉$ and $〈g,h,i〉$ are the 2 vectors

Here, we have $veca=〈-1,0,1〉$ and $vecb=〈0,1,2〉$

Therefore,

$| (veci,vecj,veck), (-1,0,1), (0,1,2) |$

$=veci| (0,1), (1,2) | -vecj| (-1,1), (0,2) | +veck| (-1,0), (0,1) |$

$=veci(-1)-vecj(-2)+veck(-1)$

$=〈-1,2,-1〉=vecc$

Verification by doing 2 dot products

$〈-1,2,-1〉.〈-1,0,1〉=1+0-1=0$

$〈-1,2,-1〉.〈0,1,2〉=0+2-2=0$

So,

$vecc$ is perpendicular to $veca$ and $vecb$

What is the cross product of [-1,0,1][-1,0,1] and [0,1,2] [0,1,2] ?