What is the cross product of #[0,8,5]# and #[1, 4, -2] #?

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Answer 1 · 2017-04-03T15:05:58

The vector is #=〈-36,5,-8〉#

The cross product is a vector perpendiculat to 2 other vectors

#| (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=〈0,8,5〉# and #vecb=〈1,4,-2〉#

Therefore,

#| (veci,vecj,veck), (0,8,5), (1,4,-2) | #

#=veci| (8,5), (4,-2) | -vecj| (0,5), (1,-2) | +veck| (0,8), (1,4) | #

#=veci(-2*8-5*4)-vecj(-2*0-5*1)+veck(0*4-8*1)#

#=〈-36,5,-8〉=vecc#

Verification by doing 2 dot products

#〈-36,5,-8〉.〈0,8,5〉=-36*0+5*8-5*8=0#

#〈-36,5,-8〉.〈1,4,-2〉=-36*1+5*4+2*8=0#

So,

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