What is the cross product of #[3, 0, 5]# and #[2, -1, 1] #?

1 Answer
Apr 10, 2018

Answer:

The vector is #=〈5,7,-3〉#

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=〈3,0,5〉# and #vecb=〈2,-1,1〉#

Therefore,

#| (veci,vecj,veck), (3,0,5), (2,-1,1) | #

#=veci| (0,5), (-1,1) | -vecj| (3,5), (2,1) | +veck| (3,0), (2,-1) | #

#=veci((0)*(1)-(-1)*(5))-vecj((3)*(1)-(2)*(5))+veck((3)*(-1)-(0)*(2))#

#=〈5,7,-3〉=vecc#

Verification by doing 2 dot products

#〈5,7,-3〉.〈3,0,5〉=(5)*(3)+(7)*(0)+(-3)*(5)=0#

#〈5,7,-3〉.〈2,-1,1〉=(5)*(2)+(7)*(-1)+(-3)*(1)=0#

So,

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