# Finding components of a vector

1. Oct 8, 2010

### snaamlsa

1. The problem statement, all variables and given/known data

You are given vectors A = 5.1i - 6.7j and B = - 3.2i + 7.2j .
A third vector C lies in the xy-plane. Vector C is perpendicular to vector A and the scalar product of C with B is 19.0

What're Cx and Cy?

The attempt at a solution
A.C = 0
B.C = 19

Last edited: Oct 8, 2010
2. Oct 8, 2010

### fzero

Can you expand both dot products in terms of the components of C?

3. Oct 8, 2010

### zgozvrm

Hint: 5.1 is the x-component of vector A, -6.7 is the y-component of vector A

4. Oct 8, 2010

### snaamlsa

thanks for the hint but it doesn't help -_-
I'm really tired of trying to solve it and I'm kinda near giving up that's why I ended up here guys so that you could help me, so please do help! I want an answer with explanation :)

this is what I got recently --> Cx = 1.34 Cy and then? I don't know what to do '~'

5. Oct 8, 2010

### fzero

You should show your work so we know where you got that from. But, that looks almost like it came from A.C = 0. Does the B.C =19 condition give another useful relationship between Cx and Cy?

6. Oct 8, 2010

### snaamlsa

oh sorry, so here is my work:

A.C = AxCx + AyCy
5.1Cx - 6.7Cy = 0
Cx = 1.34 Cy

and here we're finished with A.C and will work on B.C = 19 with the value of Cx = 1.34 Cy . . . but how?!

7. Oct 8, 2010

### fzero

Write out B.C in components and you'll get a 2nd equation for Cx and Cy. You'll have 2 equations for 2 unknowns and can combine the equations to solve for both unknowns.

8. Oct 8, 2010

### snaamlsa

I've tried that but it doesn't seem to work x_X
I think it's more of a mathematical problem than a physics one -.-

9. Oct 8, 2010

### fzero

Can you write down the equation that you obtained? If you use your 1st equation to substitute for Cx in the 2nd, you can solve for Cy. Then use that Cy in the 1st equation to give Cx.

10. Oct 8, 2010

### snaamlsa

B.C = -3.2 Cx + 7.2 Cy
is it here how should I substitute for Cx:
-3.2 (1.34) + 7.2 Cy = 19
Cy = 3.2344 (which I know is wrong)

A.C = 5.1 Cx - 6.7 Cy
5.1 Cx -6.7(3.2344) = 0
Cx = 4.2491 (which is wrong)

lol I'm not good with Maths either :\

11. Oct 8, 2010

### fzero

should be -3.2 (1.34 Cy ) + 7.2 Cy = 19

12. Oct 8, 2010

### snaamlsa

Ok I've got it
Thanks guys especially fzero, you made me think and now I got the answer by myself thanks a lot for coming back everytime I really appreciate it ^__^

13. Oct 8, 2010

### snaamlsa

lol yeah there was the real problem, I figured it out thanks a loooooooooooooooooooot!!
sorry for being an idiot :P