What is the cross product of $< - 2, 5, - 2 >$ $<-2, 5 ,-2 >$ and $< 7, 3, 2 >$ $<7 ,3 ,2 >$ ?

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Answer 1 · 2018-04-11T06:35:08

The vector is $= ⟨ 16, - 10, - 41 ⟩$ $=〈16,-10,-41〉$

The cross product of 2 vectors is calculated with the determinant

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

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

Here, we have $veca=〈-2,5,-2〉$ and $vecb=〈7,3,2〉$

Therefore,

$| (veci,vecj,veck), (-2,5,-2), (7,3,2) |$

$=veci| (5,-2), (3,2) | -vecj| (-2,-2), (7,2) | +veck| (-2,5), (7,3) |$

$=veci((5)*(2)-(-2)*(3))-vecj((-2)*(2)-(-2)*(7))+veck((-2)*(3)-(5)*(7))$

$=〈16,-10,-41〉=vecc$

Verification by doing 2 dot products

$〈16,-10,-41〉.〈-2,5,-2〉=(16)*(-2)+(-10)*(5)+(-41)*(-2)=0$

$〈16,-10,-41〉.〈7,3,2〉=(16)*(7)+(-10)*(3)+(-41)*(2)=0$

So,

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

What is the cross product of <-2, 5 ,-2 ><−2,5,−2><-2, 5 ,-2 > and <7 ,3 ,2 ><7,3,2><7 ,3 ,2 >?