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

Answer 1

Charles Aeschliman

The cross product is #=〈20,-48,2〉#

The cross product of 2 vectors, #〈a,b,c〉# and #d,e,f〉#

depends on the determinant.

#| (hati,hatj,hatk), (a,b,c), (d,e,f) | #

and # | (a,b), (c,d) |=ad-bc#

Here, the 2 vectors are #〈3,1,-6〉# and #〈7,3,2〉#

Additionally, the cross-product is

#| (hati,hatj,hatk), (3,1,-6), (7,3,2) | #

#=hati| (1,-6), (3,2) | - hatj| (3,-6), (7,2) |+hatk | (3,1), (7,3) | #

#=hati(2+18)-hati(6+42)+hatk(9-7)#

#=〈20,-48,2〉#

Verification through the use of the dot product

#〈20,-48,2〉.〈3,1,-6〉=60-48-12=0#

#〈20,-48,2〉.〈7,3,2〉=140-144+4=0#

Consequently, the vector and the other two vectors are perpendicular.

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Answer 2

Lily Adams

The cross product of <3, 1, -6> and <7, 3, 2> is < -20, -52, 16 >.

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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.

What is the cross product of #&lt;3 ,1 ,-6 &gt;# and #&lt;7 ,3 ,2 &gt;#?

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