Confused about Vector direction

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The discussion clarifies the terminology used in vector direction, specifically the phrases "north of east" and "east of north." "20 degrees north of east" indicates a counter-clockwise rotation from the east axis, while "20 degrees east of north" involves a clockwise rotation from the north axis. This distinction is crucial for accurately interpreting vector orientations in physics and mathematics. The explanation helps resolve confusion regarding vector direction naming conventions. Understanding these terms is essential for proper vector analysis.
Flaming Toilet
Hello everybody! First time poster here. Anyway, as the topic stated I'm confused about the naming of vector direction. For example, the difference between north of east and east of north?
 
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Combusting Commode

20 degrees "North of east" means "20 degrees north of the east axis. Specifically: you start with the east axis (just like the positive x axis) and rotate counter-clockwise for 20 degrees.

20 degrees "east of north" means you start with the north axis (or Y axis) and rotate clockwise 20 degrees.
 
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Likes Dng1233
Ah, I see. Thanks for your info!
 
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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