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

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Answer 1 · 2017-03-06T09:41:43

The vector is $=〈-1,-7,-2〉$

The vector perpendicular to 2 vectors is calculated with the determinant (cross product)

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

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

Here, we have $veca=〈3,-1,2〉$ and $vecb=〈1,-1,3〉$

Therefore,

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

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

$=veci(-1)-vecj(7)+veck(-2)$

$=〈-1,-7,-2〉=vecc$

Verification by doing 2 dot products

$veca.vecc$

$=〈3,-1,2>.〈-1,-7,-2〉=-3+7-4=0$

$vecb.vecc$

$=〈1,-1,3〉.〈-1,-7,-2〉=-1+7-6=0$

So,

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

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