What is the cross product of #<8, 4 ,-2 ># and #<-1, -4, 1>#?

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Answer 1 · 2017-01-19T09:32:17

The answer is #=〈-4,-6,-28〉#

The cross product of 2 vectors is calculated with the determinant

#| (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=〈8,4,-2〉# and #vecb=〈-1,-4,1〉#

Therefore,

#| (veci,vecj,veck), (8,4,-2), (-1,-4,1) | #

#=veci| (4,-2), (-4,1) | -vecj| (8,-2), (-1,1) | +veck| (8,4), (-1,-4) | #

#=veci(4-8)-vecj(8-2)+veck(-32+4)#

#=〈-4,-6,-28〉=vecc#

Verification by doing 2 dot products

#〈-4,-6,-28〉.〈8,4,-2〉=-32-24+56=0#

#〈-4,-6,-28〉.〈-1,-4,1〉=4+24-28=0#

So,

#vecc# is perpendicular to #veca# and #vecb#