What is the cross product of #<7, 2 ,6 ># and #<-3 ,5 ,-6 >#?

1 Answer
Jun 26, 2018

Answer:

The vector is #=〈-42,24,41〉 #

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=〈7,2,6〉# and #vecb=〈-3,5,-6〉#

Therefore,

#| (veci,vecj,veck), (7,2,6), (-3,5,-6) | #

#=veci| (2,6), (5,-6) | -vecj| (7,6), (-3,-6) | +veck| (7,2), (-3,5) | #

#=veci((2)*(-6)-(6)*(5))-vecj((7)*(-6)-(6)*(-3))+veck((7)*(5)-(2)*(-3))#

#=〈-42,24,41〉=vecc#

Verification by doing 2 dot products

#〈-42,24,41〉.〈7,2,6〉=(-42)*(7)+(24)*(2)+(41)*(6)=0#

#〈-42,24,41〉.〈-3,5,-6〉=(-42)*(-3)+(24)*(5)+(41)*(-6)=0#

So,

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