What is the cross product of #[2, -1, 1]# and #[3,-6,4] #?

1 Answer
Apr 19, 2018

Answer:

The vector is #=〈2,-5,-9〉#

Explanation:

The cross product of 2 vectors is calculated with the determinant

#| (veci,vecj,veck), (d,e,f), (g,h,i) | #

where #veca=〈d,e,f〉# and #vecb=〈g,h,i〉# are the 2 vectors

Here, we have #veca=〈2,-1,1〉# and #vecb=〈3,-6,4〉#

Therefore,

#| (veci,vecj,veck), (2,-1,1), (3,-6,4) | #

#=veci| (-1,1), (-6,4) | -vecj| (2,1), (3,4) | +veck| (2,-1), (3,-6) | #

#=veci((-1)*(4)-(-6)*(1))-vecj((2)*(4)-(1)*(3))+veck((2)*(-6)-(-1)*(3))#

#=〈2,-5,-9〉=vecc#

Verification by doing 2 dot products

#〈2,-5,-9〉.〈2,-1,1〉=(2)*(2)+(-5)*(-1)+(-9)*(1)=0#

#〈2,-5,-9〉.〈3,-6,4〉=(2)*(3)+(-5)*(-6)+(-9)*(4)=0#

So,

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