Does the Cross Product of -k and -i Result in +j?

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The cross product of -k and -i results in +j, as the two negative signs cancel each other out. This is equivalent to the cross product of k and i, which also yields +j. The discussion emphasizes the correct application of the cross product rules. The user expresses urgency due to an upcoming final exam. Overall, the clarification reinforces understanding of vector operations in physics.
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simple cross product question. Please help!

Homework Statement



Hey guys, I know how cross product works,

i-->j-->k : positive numbers
i<--j<--k : negative number

Homework Equations



The question that I have is, say I have -k x -i, I am supposed to get a positive j since the two negatives cancel out, is that correct? I would really appreciate any help, I have a final in less than 10 hours and would love a quick response! :)
 
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(-k)x(-i) is +j. Yes, it's the same as (k)x(i).
 


Dick said:
(-k)x(-i) is +j. Yes, it's the same as (k)x(i).


excellent! thanks for your quick response. Now, to continue studying for this nasty final! :)
 
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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