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

1 Answer
Nov 13, 2016

Answer:

The answer is #〈3,1,-5〉#

Explanation:

Let #vecu=〈1,2,1〉#

and #vecv=〈2,-1,1〉#

The cross product is given by the determinant

# ∣ ((veci,vecj,veck) , (1,2,1) , (2,-1,1)) ∣ #

#=veci(2+1)-vecj(1-2)+veck(-1-4)#

#=3veci+vecj-5veck#

#vecw=〈3,1,-5〉#

Verifications, by doing the dot product

#vecw.vecu=〈3,1,-5〉.〈1,2,1〉=3+2-5=0#

#vecw.vecv〈3,1,-5〉.〈2,-1,1〉=6-1-5=0#

So, #vecw# is perpendicular to #vecu# and #vecv#