What is the cross product of $<7 ,4 ,-3 >$ and $<-5 ,2 , -7 >$ ?

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Answer 1 · 2018-04-20T12:26:17

The vector is $=〈-22,64,34〉$

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 $veca=〈7,4,-3〉$ and $vecb=〈-5,2,-7〉$

Therefore,

$| (veci,vecj,veck), (7,4,-3), (-5,2,-7) |$

$=veci| (4,-3), (2,-7) | -vecj| (7,-3), (-5,-7) | +veck| (7,4), (-5,2) |$

$=veci((4)*(-7)-(-3)*(2))-vecj((7)*(-7)-(-3)*(5))+veck((7)*(2)-(-5)*(4))$

$=〈-22,64,34〉=vecc$

Verification by doing 2 dot products

$〈-22,64,34〉.〈7,4,-3〉=(-22)*(7)+(64)*(4)+(34)*(-3)=0$

$〈-22,64,34〉.〈-5,2,-7〉=(-22)*(-5)+(64)*(2)+(34)*(-7)=0$

So,

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

What is the cross product of <7 ,4 ,-3 ><7 ,4 ,-3 > and <-5 ,2 , -7 ><-5 ,2 , -7 >?