What is the cross product of $[1, 4, -2]$ and $[2, -1, 1]$ ?

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Answer 1 · 2017-02-22T14:14:36

The result is $=〈2,-5,-9〉$

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 $veca=〈1,4,-2〉$ and $vecb=〈2,-1,1〉$

Therefore,

$| (veci,vecj,veck), (1,4,-2), (2,-1,1) |$

$=veci| (4,-2), (-1,1) | -vecj| (1,-2), (2,1) | +veck| (1,4), (2,-1) |$

$=veci(2)-vecj(5)+veck(-9)$

$=〈2,-5,-9〉=vecc$

Verification by doing 2 dot products

$veca.vecc$

$=〈1,4,-2>.〈2,-5,-9〉=2-20+18=0$

$vecb.vecc$

$=〈2,-1,1〉.〈2,-5,-9〉=4+5-9=0$

So,

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

What is the cross product of [1, 4, -2][1, 4, -2] and [2, -1, 1] [2, -1, 1] ?