What is the cross product of $< 10, 4, 1 >$ $<10 ,4 ,1 >$ and $< - 5, 2, 3 >$ $<-5 ,2 ,3 >$ ?

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Answer 1 · 2018-03-02T06:28:47

The vector is $= ⟨ 10, - 35, 40 ⟩$ $=〈10,-35,40〉$

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 $veca=〈10,4,1〉$ and $vecb=〈-5,2,3〉$

Therefore,

$| (veci,vecj,veck), (10,4,1), (-5,2,3) |$

$=veci| (4,1), (2,3) | -vecj| (10,1), (-5,3) | +veck| (10,4), (-5,2) |$

$=veci((4)*(3)-(1)*(2))-vecj((10)*(3)+(5)*(1))+veck((10)*(2)-(4)*(-5))$

$=〈10,-35,40〉=vecc$

Verification by performing 2 dot products

$〈10,4,1〉.〈10,-35,40〉=(10)*(10)+(4)*(-35)+(1)*(40)=0$

$〈-5,2,3〉.〈10,-35,40〉=(-5)*(10)+(2)*(-35)+(3)*(40)=0$

So,

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

What is the cross product of <10 ,4 ,1 ><10,4,1><10 ,4 ,1 > and <-5 ,2 ,3 ><−5,2,3><-5 ,2 ,3 >?