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

1 Answer
Jun 24, 2017

Answer:

The vector is #=〈-42,-33,-37〉#

Explanation:

The cross product of #2# vectors is a vector perpendicular to the #2# vectors. It 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=〈4,5,-9〉# and #vecb=〈5,-3,-3〉#

Therefore,

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

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

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

#=〈-42,-33,-37〉=vecc#

Verification by doing 2 dot products

#〈-42,-33,-37〉.〈4,5,-9〉=-42*4-33*5+37*9=0#

#〈-42,-33,-37〉.〈5,-3,-3〉=-42*5+33*3+37*3=0#

So,

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