What is the cross product of $[3, 2, 5]$ and $[4,3,6]$ ?

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Answer 1 · 2017-03-08T15:53:24

The vector is $=〈-3,2,1〉$

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 $veca=〈3,2,5〉$ and $vecb=〈4,3,6〉$

Therefore,

$| (veci,vecj,veck), (3,2,5), (4,3,6) |$

$=veci| (2,5), (3,6) | -vecj| (3,5), (4,6) | +veck| (3,2), (4,3) |$

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

$=〈-3,2,1〉=vecc$

Verification by doing 2 dot products

$veca.vecc$

$=〈3,2,5>.〈-3,2,1〉=-9+4+5=0$

$vecb.vecc$

$=〈4,3,6〉.〈-3,2,1〉=-12+6+6=0$

So,

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

What is the cross product of [3, 2, 5][3, 2, 5] and [4,3,6] [4,3,6] ?