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

• snaamlsa
In summary: 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 ^__^sorry for being an idiot :P
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 Cx and Cy?

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

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

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

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 '~'

snaamlsa said:
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 '~'

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?

fzero said:
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?

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?!

snaamlsa said:
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?!

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.

fzero said:
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.

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 -.-

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.

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 :\

snaamlsa said:
-3.2 (1.34) + 7.2 Cy = 19

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

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 ^__^

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

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

## 1. What are the two main components of a vector?

The two main components of a vector are magnitude and direction. Magnitude refers to the length or size of the vector, while direction refers to the angle at which the vector is pointing.

## 2. How do you find the magnitude of a vector?

To find the magnitude of a vector, you can use the Pythagorean theorem. This involves squaring the x and y components of the vector, adding them together, and then taking the square root of the sum. The resulting value is the magnitude of the vector.

## 3. How do you determine the direction of a vector?

The direction of a vector can be determined by using trigonometric functions such as sine, cosine, and tangent. These functions allow you to calculate the angle at which the vector is pointing in relation to the positive x-axis.

## 4. Can vectors have negative components?

Yes, vectors can have negative components. This means that the vector is pointing in the opposite direction of the positive x or y-axis. Negative components can be represented as -x or -y, depending on the direction of the vector.

## 5. How do you find the components of a vector given its magnitude and direction?

To find the components of a vector, you can use trigonometric functions and basic geometry. For example, if you know the magnitude and direction of a vector, you can calculate the x and y components by using sine and cosine. Alternatively, you can also use the magnitude and direction to create a right triangle and use the Pythagorean theorem to find the components.

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