Finding the components of a Cartesian vector

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The discussion revolves around solving a Cartesian vector problem, where the user believes their calculations are correct but the computer indicates an error. The user calculated the components as Fz=530.33N, F’=530.33N, Fx=256.165N, and Fy=-459.28N, resulting in the vector F=(256.165i-459.28j+530.33k)N. Despite their confidence in the calculations, the user received feedback about checking signs and is hesitant to guess due to potential point deductions. Other participants suggest that the issue may lie in the expected format rather than the calculations themselves and recommend consulting the instructor for clarification. The conversation highlights the importance of understanding both the calculations and the submission requirements in vector problems.
JON123
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Homework Statement



Picture is attached

Homework Equations


The Attempt at a Solution



I feel like I am right and the computer is wrong, but I just wanted to check here first. I attached a picture of the problem and my answer.

This is how I solved the problem:

Fz=750sin(45)=530.33N
F’=750cos(45)=530.33N
Fx=F’cos(60)=256.165N
Fy=F’sin(60)=-459.28N

So my answer was: F=(256.165i-459.28j+530.33k)N and it says it's wrong. When i first submitted it, it said check signs, but i don't want to just guess at the signs because it takes off points for wrong answers, and i would like to know what I'm doing wrong.
 

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It looks like you calculated the components correctly. If the computer says you are wrong, maybe it expects a different format from the one you used. I think you should your instructor for clarifications.
 
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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