The magnitude and the resultant vector

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Magnitude refers to a scalar value that represents the size or quantity of a vector, while the resultant vector is the vector sum of two or more vectors. In the context of vector addition, the magnitude of the resultant vector can be calculated, but they are not the same thing. For instance, if a car's velocity is 12 m/s [east], 12 m/s is the magnitude, whereas the resultant vector would include both the magnitude and direction. Understanding the distinction between magnitude and resultant vectors is crucial in physics and vector analysis.
chocolatelover
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Hi everyone,

Could someone please tell me if the magnitude is the same thing as the resultant vector? I know how to solve for the magnitude, but isn't it the same thing as the resultant vector A+B?

Thank you very much
 
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Yes, it is the same thing.

Magnitude is defined as a scalar value having physical units.

so for example, if a car's velocity is 12m/s [east]

then 12 would be its magnitude.
 
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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