What is the cross product of #<-1, 2 ,0 ># and #<-3 ,1 ,9 >#?

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Answer 1 · 2017-02-20T16:29:27

The answer is #=〈18,9,5〉#

The vector perpendicular to 2 vectors is calculated with the determinant (cross product)

#| (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=〈-1,2,0〉# and #vecb=〈-3,1,9〉#

Therefore,

#| (veci,vecj,veck), (-1,2,0), (-3,1,9) | #

#=veci| (2,0), (1,9) | -vecj| (-1,0), (-3,9) | +veck| (-1,2), (-3,1) | #

#=veci(18)-vecj(-9)+veck(-1+6)#

#=〈18,9,5〉=vecc#

Verification by doing 2 dot products

#〈-1,2,0>.〈18,9,5〉=-18+18=0#

#〈-3,1,9〉.〈18,9,5〉=-54+9+45=0#

So,

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