Clear up some cross product confusion for me

2slowtogofast

Here is what I have

A=xro+yr1

B=yro+xr1

I need to find A x B

I am confused about do it because The components of A and B are in terms of vectors

If A = 3i + 4j + 7k and B = 2i + 2j + 1k I would have no problem (these numbers are meaningless just giving an example) finding A x B but I don't have components I have vectors. Can some one explain how to do this. Thanks

2slowtogofast

Could I set it up as follows

Sorry I don't no how to input a matrix hopefully this can get the idea across
ro r1 k ro r1
x y 0 x y
y x 0 y x

and then do the normal cross product thing where you multiply diagonals and so on. The thing that troubles me is there is really no k component. The only thing I know is my answer will be perpindicular to the plane with r0 and r1 so not sure what to do

mathman

AXB = (x² - y²)r0Xr1.

I am assuming x and y are scalars.

tiny-tim

hi 2slowtogofast!
hints: distributive law

what are ro x ro and r1 x r1 ?

2slowtogofast

@tinytim

roxro = 0 I can see how that will simplify things I am confused about the distributive law part

A x (B+D) = (AxB)+(AxD)

I have somthing more like this

(xro+yr1) x (yro+xr1) = (xro+yr1) x yro + (xro+yr1) x xr1

Use the distributive rule again on the RHS

(xro x yro) + (yr1 x yro) + (xro x xr1) + (yr1 x r1)

Then the first and last terms are 0. Am on the right track or did I make a wrong turn somewhere

tiny-tim

hi 2slowtogofast!

(just got up )
yes

now what is the relationship between r1 x ro and ro x r1 ?

2slowtogofast

r0 x r1 = -(r1 x r0)

If that is correct i think i can take it from there thanks for the help

tiny-tim

that's it!