Associative Operation with Four Vectors: Is it True?

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The discussion centers on the validity of an associative operation involving four vectors, specifically questioning the equation 2*(p+p_1)p_3(p+p_1)p_2 - (p_3)(p_2)(p+p_1)^2 = (p_3)(p_2)(p+p_1)^2. Participants express confusion over the multiplication order and suggest using LaTeX for clarity. An attachment is provided to illustrate the problem further. The main focus is on determining whether the operation is associative. The conversation highlights the complexities involved in vector operations and the need for clear mathematical representation.
bgy
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hi,

Is it true that

2*(p+p_1)p_3(p+p_1)p_2 - (p_3)(p_2)(p+p_1)^2 = (p_3)(p_2)(p+p_1)^2 ,

where p,p_1,p_2,p_3 are four vectors? Or simply: associative this operation?
 
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cant quite figure out what u are multiplying by what
why don't u try using latex format
 
esalihm said:
cant quite figure out what u are multiplying by what
why don't u try using latex format

ok. See the attachment.
 

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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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