Phyiscs, finding components with per. line

[Crusaderking1]

Homework Statement

You are given vectors A= 5.1 { i } - 7.0 { j } and vec B= - 3.8 { i } + 7.3{j}. A third vector C lies in the xy-plane. Vector C is perpendicular to vector A and the scalar product of vec C with vec B is 16.0.

Find the x -component and y-component of vector vec C

Homework Equations

Not sure, I have no idea how to find components of C with no angles given. I used the Pythagorean theorem for finding the magnitudes of A and B, however, I do not know how/if that even helps.

The Attempt at a Solution

Ok, for an attempt, I found the magnitude of A to be 8.6023 m while the magnitude of B to be 8.2293 m. I have tried to find C, but I have many different answers I keep getting, all around 5.0 meters, but definitely not right. I finally reached an answer of -2.04 m for the x-component, and it was utterly wrong.

I really need help. thanks. If you need me to clear anything up, just ask.

 

[gneill]

You'll want to take advantage of the properties of the dot product (scalar product) for this problem. Do you know how to calculate the dot product of two vectors from their components?

In order for two vectors to be perpendicular, what must be the value of their dot product?

 

[Crusaderking1]

You'll want to take advantage of the properties of the dot product (scalar product) for this problem. Do you know how to calculate the dot product of two vectors from their components?

In order for two vectors to be perpendicular, what must be the value of their dot product?

Yes, I know that vector A*B = AxBx + AyBy + AzBz, but I don't understand how I'm suppose to find C components by using scalar products.

(-3.81 i)(x)+(7.3 i)(y) = 16.0 meters.

B*C = 16.0 meter(scalar product)

However, how do I find X or Y this way?
Thats where I have issues finding the components of C.

 

[EnjoiTAD]

What he was trying to say is the dot product of two perpendicular vectors is 0

 

[Crusaderking1]

Does than mean that the C x-component and y-component are zero?

 

[EnjoiTAD]

No A doted with C equals 0 then B doted with C = 16. I'm not positive but I'm sure you could just use a simple linear system to figure it out.

 

[Crusaderking1]

No A doted with C equals 0 then B doted with C = 16. I'm not positive but I'm sure you could just use a simple linear system to figure it out.

Alright, I see what you mean, but then I just get led back to my original equation of B*C =16.0 with 2 variables, which I don't know how to put two and two together(A*C = 0, B*C=16).

 

[EnjoiTAD]

Thats just it have you solved linear systems before? I worked it out it works.
5.1x-7.0y=0
-3.8x+7.3y=16
just solve that.

 

[Crusaderking1]

No A doted with C equals 0 then B doted with C = 16. I'm not positive but I'm sure you could just use a simple linear system to figure it out.

Thats just it have you solved linear systems before? I worked it out it works.
5.1x-7.0y=0
-3.8x+7.3y=16
just solve that.

Thanks a lot! Really appreciate it.

However, if anyone want to show me how to do the problem using a different method, that would be great.