How to Find Cx and Cy Given Perpendicular and Scalar Product Conditions?

[snaamlsa]

Homework Statement

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 C_x and C_y?

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

 

[fzero]

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

 

[zgozvrm]

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

 

[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 --> C_x = 1.34 C_y and then? I don't know what to do '~'

 

[fzero]

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 --> C_x = 1.34 C_y and then? I don't know what to do '~'

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 C_x and C_y?

 

[snaamlsa]

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 C_x and C_y?

oh sorry, so here is my work:

A.C = A_xC_x + A_yC_y
5.1C_x - 6.7C_y = 0
C_x = 1.34 C_y

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

 

[fzero]

oh sorry, so here is my work:

A.C = A_xC_x + A_yC_y
5.1C_x - 6.7C_y = 0
C_x = 1.34 C_y

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

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

 

[snaamlsa]

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

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 -.-

 

[fzero]

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

 

[snaamlsa]

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

A.C = 5.1 C_x - 6.7 C_y
5.1 C_x -6.7(3.2344) = 0
C_x = 4.2491 (which is wrong)

lol I'm not good with Maths either :\

 

[fzero]

-3.2 (1.34) + 7.2 C_y = 19

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

 

[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 ^__^

 

[snaamlsa]

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

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