What is the cross product of #(2i -3j + 4k)# and #(4 i + 4 j + 2 k)#?

1 Answer
May 13, 2018

Answer:

The vector is #=〈-22,12,20〉#

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,-3,4〉# and #vecb=〈4,4,2〉#

Therefore,

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

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

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

#=〈-22,12,20〉=vecc#

Verification by doing 2 dot products

#〈-22,12,20〉.〈2,-3,4〉=(-22)*(2)+(12)*(-3)+(20)*(4)=0#

#〈-22,12,20〉.〈4,4,2〉=(-22)*(4)+(12)*(4)+(20)*(2)=0#

So,

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