Vector Subtraction Homework Help

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Vector subtraction can be understood as adding the opposite of a vector, expressed mathematically as a + (-b) = a - b. The confusion arises in distinguishing between the operations, with the correct formula for vector subtraction being r = t - s, rather than r = s - t. The triangle method illustrates that when vectors are added, the resultant vector can be represented as r + s = t. This visual approach helps clarify the relationship between the vectors involved in subtraction. Understanding these principles is essential for solving vector subtraction problems accurately.
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Homework Statement


vector subtraction


Homework Equations


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The Attempt at a Solution


I'm really confused when it comes to subtraction, the following problems seems like an addition problem and i thought it was r+s=t, but i got it wrong. Any help would be gladly appreciated.
 

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You can think the subtraction the vector b from a as addition of the opposite of b, (-b) to a: a+b= a+(-b)

ehild
 
i think i got it, is it r=s-t?
 
No, r=t-s. If you use the triangle method for addition you see from the figure that r+s=t. So r=t-s.

ehild
 
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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