What is the cross product of #<4 , 5 ,-9 ># and #<4, 3 ,-3 >#?

1 Answer
Mar 18, 2018

Answer:

The vector is #<12, -24, -8>#

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=〈4,5,-9〉# and #vecb=〈4,3,-3〉#

Therefore,

#| (veci,vecj,veck), (4,5,-9), (4,3,-3) | #

#=veci| (5,-9), (3,-3) | -vecj| (4,-9), (4,-3) | +veck| (4,5), (4,3) | #

#=veci((5)*(-3)-(9)*(-3))-vecj((4)*(-3)-(9)*(4))+veck((4)*(3)-(4)*(5))#

#=〈12,-24,-8〉=vecc#

Verification by doing 2 dot products

#〈12,-24,-8〉.〈4,5,-9〉=(12)*(4)+(-24)*(5)+(-8)*(-9)=0#

#〈12,-24,-8〉.〈4,3,-3〉=(12)*(4)+(-24)*(3)+(-8)*(-3)=0#

So,

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