What is the cross product of $< - 3, - 6, - 3 >$ $<-3 ,-6 ,-3 >$ and $< - 2, 1, - 7 >$ $<-2 ,1 , -7 >$ ?

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Answer 1 · 2017-04-09T07:49:30

The vector is $= ⟨ 45, - 15, - 15 ⟩$ $=〈45,-15,-15〉$

The cross product of 2 vectors is

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

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

Here, we have $veca=〈-3,-6,-3〉$ and $vecb=〈-2,1,-7〉$

Therefore,

$| (veci,vecj,veck), (-3,-6,-3), (-2,1,-7) |$

$=veci| (-6,-3), (1,-7) | -vecj| (-3,-3), (-2,-7) | +veck| (-3,-6), (-2,1) |$

$=veci(-6*-7+3*1)-vecj(-3*-7-3*2)+veck(-3*1-6*2)$

$=〈45,-15,-15〉=vecc$

Verification by doing 2 dot products

$〈45,-15,-15〉.〈-3,-6,-3〉=-45*3+6*15+3*15=0$

$〈45,-15,-15〉.〈-2,1,-7〉=-45*2-15*1+15*7=0$

So,

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

What is the cross product of <-3 ,-6 ,-3 ><−3,−6,−3><-3 ,-6 ,-3 > and <-2 ,1 , -7 ><−2,1,−7><-2 ,1 , -7 >?