What is the cross product of #[3, 1, -4]# and #[3, -4, 2] #?

1 Answer
Nov 17, 2016

Answer:

The vector is #=〈-14,-18,-15〉#

Explanation:

Let #vecu=〈3,1,-4〉# and #vecv=〈3,-4,2〉 #

The cross product is given by the determinant

#vecu# x #vecv# #= | (veci,vecj,veck), (3,1,-4), (3,-4,2) | #

#= veci| (1,-4), (-4,2) | -vecj | (3,-4), (3,2) | +veck | (3,1), (3,-4) | #

#=veci(2-16)+vecj(-6-12)+veck(-12-3)#

#=vecw=〈-14,-18,-15〉#

Verification, the dot products must de #0#

#vecu.vecw=〈3,1,-4〉.〈-14,-18,-15〉=(-42-18+60)=0#

#vecv.vecw=〈3,-4,2〉.〈-14,-18,-15〉=(-42+72-30)=0#

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