What is the cross product of $<7, 2 ,6 >$ and $<-3 ,5 ,-6 >$ ?

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Answer 1 · 2018-06-26T05:30:09

The vector is $=〈-42,24,41〉$

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 $veca=〈7,2,6〉$ and $vecb=〈-3,5,-6〉$

Therefore,

$| (veci,vecj,veck), (7,2,6), (-3,5,-6) |$

$=veci| (2,6), (5,-6) | -vecj| (7,6), (-3,-6) | +veck| (7,2), (-3,5) |$

$=veci((2)*(-6)-(6)*(5))-vecj((7)*(-6)-(6)*(-3))+veck((7)*(5)-(2)*(-3))$

$=〈-42,24,41〉=vecc$

Verification by doing 2 dot products

$〈-42,24,41〉.〈7,2,6〉=(-42)*(7)+(24)*(2)+(41)*(6)=0$

$〈-42,24,41〉.〈-3,5,-6〉=(-42)*(-3)+(24)*(5)+(41)*(-6)=0$

So,

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

What is the cross product of <7, 2 ,6 ><7, 2 ,6 > and <-3 ,5 ,-6 ><-3 ,5 ,-6 >?