What is the cross product of #<10 ,4 ,1 ># and #<-5 ,2 ,3 >#?

1 Answer
Mar 2, 2018

Answer:

The vector is #=〈10,-35,40〉#

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=〈10,4,1〉# and #vecb=〈-5,2,3〉#

Therefore,

#| (veci,vecj,veck), (10,4,1), (-5,2,3) | #

#=veci| (4,1), (2,3) | -vecj| (10,1), (-5,3) | +veck| (10,4), (-5,2) | #

#=veci((4)*(3)-(1)*(2))-vecj((10)*(3)+(5)*(1))+veck((10)*(2)-(4)*(-5))#

#=〈10,-35,40〉=vecc#

Verification by performing 2 dot products

#〈10,4,1〉.〈10,-35,40〉=(10)*(10)+(4)*(-35)+(1)*(40)=0#

#〈-5,2,3〉.〈10,-35,40〉=(-5)*(10)+(2)*(-35)+(3)*(40)=0#

So,

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