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

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Answer 1 · 2016-12-21T06:30:23

The answer is #=〈-11,-20,-5〉#

The cross product is obtained from the determinant

# | (hati,hatj,hatk), (d,e,f), (g,h,i) | #

where #〈d,e,f〉# and #〈g,h,i〉# are the 2 vectors.

Therefore,

# | (hati,hatj,hatk), (5,-3,1), (-5,2,3) | #

#=hati | (-3,1), (2,3) |-hatj | (5,1), (-5,3) |+hatk | (5,-3), (-5,2) |#

#=hati(-3*3-2*1)-hatj(5*3+5*1)+hatk(5*2-5*3)#

#=hati(-11)-hatj()20+hatk(-5)#

#=〈-11,-20,-5〉#

Verification , by doing a dot product

#〈-11,-20,-5〉.〈5,-3,1〉=(-55+60-5)=0#

#〈-11,-20,-5〉.〈-5,2,3〉=(55-40-15)=0#