What is the cross product of $< 8, 4, - 2 >$ $<8, 4 ,-2 >$ and $< - 1, - 4, 1 >$ $<-1, -4, 1>$ ?

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Answer 1 · 2017-01-19T09:32:17

The answer is $= ⟨ - 4, - 6, - 28 ⟩$ $=〈-4,-6,-28〉$

The cross product of 2 vectors 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 $veca=〈8,4,-2〉$ and $vecb=〈-1,-4,1〉$

Therefore,

$| (veci,vecj,veck), (8,4,-2), (-1,-4,1) |$

$=veci| (4,-2), (-4,1) | -vecj| (8,-2), (-1,1) | +veck| (8,4), (-1,-4) |$

$=veci(4-8)-vecj(8-2)+veck(-32+4)$

$=〈-4,-6,-28〉=vecc$

Verification by doing 2 dot products

$〈-4,-6,-28〉.〈8,4,-2〉=-32-24+56=0$

$〈-4,-6,-28〉.〈-1,-4,1〉=4+24-28=0$

So,

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

What is the cross product of <8, 4 ,-2 ><8,4,−2><8, 4 ,-2 > and <-1, -4, 1><−1,−4,1><-1, -4, 1>?