What is the cross product of #[-1,0,1]# and #[0,1,2] #?

1 Answer
Jan 17, 2017

Answer:

The cross product is #=〈-1,2,-1〉#

Explanation:

The cross product 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=〈-1,0,1〉# and #vecb=〈0,1,2〉#

Therefore,

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

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

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

#=〈-1,2,-1〉=vecc#

Verification by doing 2 dot products

#〈-1,2,-1〉.〈-1,0,1〉=1+0-1=0#

#〈-1,2,-1〉.〈0,1,2〉=0+2-2=0#

So,

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