How do you find the cross product and verify that the resulting vectors are perpendicular to the given vectors #<-3,-1,2>times<4,-4,0>#?

1 Answer
Oct 28, 2016

Answer:

The cross product #〈8,8,16〉#

Explanation:

The cross product of 2 vectors #vecu=〈u_1,u_2,u_3〉# and #vecv=〈v_1,v_2,v_3〉# is given by

#vecu#x#vecv# #=〈u_2v_3-u_3v_2,u_3v_1-u_1v_3,u_1v_2-u_2v_1〉#
This vector is perpendicular to #vecu# and #vecv#

So the cross product of #〈-3,-1,2〉# and #〈4,-4,0〉# is #〈8,8,16〉#

Verification by making the dot product
#〈-3,-1,2〉.〈8,8,16〉=-24-8+32=0#
and #〈4,-4,0〉.〈8,8,16〉=32-32+0=0#

As both dot products are #=0# so the vector is perpendicular to the other 2 vectors