What is the cross product of #<-3 ,-6 ,-3 ># and #<-2 ,1 , -7 >#?

1 Answer
Apr 9, 2017

Answer:

The vector is #=〈45,-15,-15〉#

Explanation:

The cross product of 2 vectors is

#| (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=〈-3,-6,-3〉# and #vecb=〈-2,1,-7〉#

Therefore,

#| (veci,vecj,veck), (-3,-6,-3), (-2,1,-7) | #

#=veci| (-6,-3), (1,-7) | -vecj| (-3,-3), (-2,-7) | +veck| (-3,-6), (-2,1) | #

#=veci(-6*-7+3*1)-vecj(-3*-7-3*2)+veck(-3*1-6*2)#

#=〈45,-15,-15〉=vecc#

Verification by doing 2 dot products

#〈45,-15,-15〉.〈-3,-6,-3〉=-45*3+6*15+3*15=0#

#〈45,-15,-15〉.〈-2,1,-7〉=-45*2-15*1+15*7=0#

So,

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