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Clear up some cross product confusion for me

by 2slowtogofast
Tags: clear, confusion, cross, product
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2slowtogofast
#1
Feb19-12, 01:34 PM
P: 132
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
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2slowtogofast
#2
Feb19-12, 01:47 PM
P: 132
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
#3
Feb20-12, 04:10 PM
Sci Advisor
P: 6,058
AXB = (x2 - y2)r0Xr1.

I am assuming x and y are scalars.

tiny-tim
#4
Feb20-12, 04:28 PM
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P: 26,148
Clear up some cross product confusion for me

hi 2slowtogofast!
Quote Quote by 2slowtogofast View Post
Here is what I have

A=xro+yr1

B=yro+xr1


I need to find A x B
hints: distributive law
what are ro x ro and r1 x r1 ?
2slowtogofast
#5
Feb20-12, 08:08 PM
P: 132
@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
#6
Feb21-12, 04:44 AM
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P: 26,148
hi 2slowtogofast!

(just got up )
Quote Quote by 2slowtogofast View Post
(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
yes

now what is the relationship between r1 x ro and ro x r1 ?
2slowtogofast
#7
Feb21-12, 06:12 PM
P: 132
r0 x r1 = -(r1 x r0)

If that is correct i think i can take it from there thanks for the help
tiny-tim
#8
Feb22-12, 03:18 AM
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Quote Quote by 2slowtogofast View Post
r0 x r1 = -(r1 x r0)
that's it!


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