Question

Prove the following properties of the cross product: u × v = - (v × u )

Answer 1

All you need to do is make u equal to vector a_1,a_2,a_3 and vector v equal b_1,b_2,b_3 and use the properties of the cross product rules to help

Answer 2

ohhh so i should use the cross product Mnemonic Device? to prove it?

Answer 3

Let me quickly do this one really quick just to give myself a refresher as to what exactly you need to do

Answer 4

But I meant just do the cross product of the 2 vectors I gave you

Answer 5

okay thanks very much :)

Answer 6

but since its negative, wouldnt that change the vectors?

Answer 7

You have to pay attention though to the fact that the first is u cross v and the second one is doing v cross u

Answer 8

And to answer your question....multiplying a vector by a negative 1 would just make it a vector that would point in the opposite direction of its original vector but it would still be the same vector

Answer 9

ohhhh right! thanks..that really helps

Answer 10

this is what i got for u x v =
u2v3-u3v2 , u3v1-u1v3 , u1v2-u2v1

Answer 11

Yup thats what I got

Answer 12

Now do the cross product of the other and once you have that cross product....multiple your solution for that one by a negative one

Answer 13

okay now i got it! thanks!

Answer 14

No problem