What is the cross product of #[3,-1,2]# and #[1,-1,3] #?

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Answer 1 · 2017-03-06T09:41:43

The vector is #=〈-1,-7,-2〉#

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=〈3,-1,2〉# and #vecb=〈1,-1,3〉#

Therefore,

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

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

#=veci(-1)-vecj(7)+veck(-2)#

#=〈-1,-7,-2〉=vecc#

Verification by doing 2 dot products

#veca.vecc#

#=〈3,-1,2>.〈-1,-7,-2〉=-3+7-4=0#

#vecb.vecc#

#=〈1,-1,3〉.〈-1,-7,-2〉=-1+7-6=0#

So,

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