What is the cross product of #<-1, 2 ,27 ># and #<-3 ,1 ,-1 >#?

1 Answer
Dec 29, 2016

Answer:

The answer is #=〈-29,-82,5〉#

Explanation:

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

is given by the determinant

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

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

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

Here, the 2 vectors are #〈-1,2,27〉# and #〈-3,1,-1〉#

And the cross product is

#| (hati,hatj,hatk), (-1,2,27), (-3,1,-1) | #

#=hati| (2,27), (1,-1) | - hatj| (-1,27), (-3,-1) |+hatk | (-1,2), (-3,1) | #

#=hati(-2-27)-hati(1+81)+hatk(-1+6)#

#=〈-29,-82,5〉#

Verification, by doing the dot product

#〈-29,-82,5〉.〈-1,2,27〉=29-164+135=0#

#〈-29,-82,5〉.〈-3,1,-1〉=87-82-5=0#

Therefore, the vector is perpendicular to the other 2 vectors