How do I find the components of a vector parallel to the x-axis?

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To find the components of a vector parallel to the x-axis, recognize that it will only have an x component and no y component. The x component is equal to the length of the vector itself. Trigonometric functions are not necessary in this case since the vector's direction is aligned with the x-axis. This simplifies the calculation, as the y component is zero. Understanding this concept is crucial for solving related physics problems effectively.
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Hi --

I'm working on a physics problem that involves adding several vectors. I know that to find the components of a vector you must do some trig with the angle the vector makes with the x-axis. However, one of the vectors is parallel to the x-axis (but not actually laying ON the x-axis). I'm not sure where to go from there; how to find its components. I tried a few things, but none of them seem to give me the correct answer.

Can anyone help me out with this?
 
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The vector will simply have an x component and no y component.
 
Hmm, ok. Will the x component just be the length of the vector then?
 
Yes, you're right.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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