What is the cross product of #[1, 4, -2]# and #[2, -1, 1] #?

1 Answer
Feb 22, 2017

Answer:

The result is #=〈2,-5,-9〉#

Explanation:

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=〈1,4,-2〉# and #vecb=〈2,-1,1〉#

Therefore,

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

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

#=veci(2)-vecj(5)+veck(-9)#

#=〈2,-5,-9〉=vecc#

Verification by doing 2 dot products

#veca.vecc#

#=〈1,4,-2>.〈2,-5,-9〉=2-20+18=0#

#vecb.vecc#

#=〈2,-1,1〉.〈2,-5,-9〉=4+5-9=0#

So,

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