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#