Is Calculating Z-Axis Components the Same as X and Y Components?

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Calculating scalar components for the z-axis follows the same principles as for the x and y components. To find these components, one can use trigonometric functions based on the angle provided. In the example given, an acceleration vector of 9.81 m/s² at a 75-degree angle with the positive z-axis can be resolved into parallel and perpendicular components. The method remains consistent across all three axes, confirming that the approach is indeed the same. Understanding these calculations is essential for working with 3D vectors effectively.
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Hey, I'm just wondering if i need to find scalar components for a magnitude on the z-axis, do i go about the same way i would with regual x,y compenents, or is there something else that i need to do??

and just for clarification, the z-axis is the one that makes it 3D, like it's 'popping' out at you??

Thanks!
 
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What is the problem specifically?
 
the problem is:

An acceleration vector of magnitude 9.81m/s^2 makes an angle of 75 degress with the positive z-axis. Find the scalar components of the vector parallel and perpendicular to the z-axis.
 
Then I would answer 'yes' to your original question. :-)
 
thanks for your help
 
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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