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

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Answer 1 · 2017-07-31T09:36:41

The vector is #=〈-7,-4,1〉#

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=〈1,-2,-1〉# and #vecb=〈1,-1,3〉#

Therefore,

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

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

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

#=〈-7,-4,1〉=vecc#

Verification by doing 2 dot products

#〈1,-2,-1〉.〈-7,-4,1〉=-7*1+2*4-1*1=0#

#〈1,-2,-1〉.〈1,-1,3〉=1*1+1*2-1*3=0#

So,

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