Pythagorean triplet and vectors

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Vectors A, B, and C can relate through the equation A - B = C, which is illustrated using the Pythagorean triplet 3, 4, 5. The discussion explores whether C can equal A + B, suggesting that this is feasible when considering vectors in opposite directions. The confusion arises from interpreting vector subtraction strictly in terms of triangles. Ultimately, the relationship between the vectors depends on their magnitudes and directions. Understanding these vector relationships is crucial for applying concepts of vector addition and subtraction effectively.
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Suppose that vectors A, B and C are related by A-B=C.

a) Is it possible that A-B=C? If so, draw the sort of situation when this is so. (A is the magnitude of A, B of B and C of C.)

b) Is it possible that C=A+B? If so, then draw the sort of situation when this is so.

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a) I used the Pythagorean triplet 3,4,5 for this situation.
b) I'm not sure but I think the question basically asks whether C can equal A+B and at the same time can C equal the square root of the sum of the squares of A and B. I'm having trouble getting my head around this.
 
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OK never mind, false alarm. For some reason I was thinking strictly in the form of triangles for my vector subtraction. I believe situation b) is possible if you have any two vectors of opposite direction.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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