What is the cross product of #[1,-2,-1]# and #[-2,0,3] #?

1 Answer
Jan 6, 2017

Answer:

The answer is #=〈-6,-1,-4〉#

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,-1〉# and #〈-2,0,3〉#

And the cross product is

#| (hati,hatj,hatk), (1,-2,-1), (-2,0,3) | #

#=hati| (-2,-1), (0,3) | - hatj| (1,-1), (-2,3) |+hatk | (1,-2), (-2,0) | #

#=hati(-6+0)-hati(3-2)+hatk(0-4)#

#=〈-6,-1,-4〉#

Verification, by doing the dot product

#〈-6,-1,-4〉.〈1,-2,-1〉=-6+2+4=0#

#〈-6,-1,-4〉.〈-2,0,3〉=12+0-12=0#

Therefore, the vector is perpendicular to the other 2 vectors