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What is the cross product of #[1, 3, 4]# and #[3, 7, 9]#?

Answer 1

Leo Abeyta

The vector is #=〈-1,3,-2〉#

Two vectors' cross product 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=〈1,3,4〉# and #vecb=〈3,7,9〉#

Consequently,

#| (veci,vecj,veck), (1,3,4), (3,7,9) | #

#=veci| (3,4), (7,9) | -vecj| (1,4), (3,9) | +veck| (1,3), (3,7) | #

#=veci(3*9-4*7)-vecj(1*9-4*3)+veck(1*7-3*3)#

#=〈-1,3,-2〉=vecc#

Verification using the two dot method

#〈-1,3,-2〉.〈1,3,4〉=-1*1+3*3-2*4=0#

#〈-1,3,-2〉.〈3,7,9〉=-1*3+3*7-2*9=0#

Thus,

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

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Answer 2

Leo Abeyta

The cross product of [1, 3, 4] and [3, 7, 9] is [-3, -3, 4].

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.