What is the cross product of $[-3, 1, -1]$ and $[0,1,2]$ ?

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Answer 1 · 2017-07-11T08:41:48

The vector is $=〈3,6,-3〉$

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 $veca=〈-3,1,-1〉$ and $vecb=〈0,1,2〉$

Therefore,

$| (veci,vecj,veck), (-3,1,-1), (0,1,2) |$

$=veci| (1,-1), (1,2) | -vecj| (-3,-1), (0,2) | +veck| (-3,1), (0,1) |$

$=veci(1*2+1*1)-vecj(-3*2+0*1)+veck(-3*1-0*1)$

$=〈3,6,-3〉=vecc$

Verification by doing 2 dot products

$〈3,6,-3〉.〈-3,1,-1〉=-3*3+6*1+3*1=0$

$〈3,6,-3〉.〈0,1,2〉=3*0+6*1-3*2=0$

So,

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

What is the cross product of [-3, 1, -1][-3, 1, -1] and [0,1,2] [0,1,2] ?