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Regular Math Addition:

432+53=485

Vector Addition:

if u=<a,b> and v=<c,d>

then u+v=<a+c,b+d>

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Q: What is the difference between regular math addition and vector addition?
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What is the difference between vector addition and algebraic addition?

There is no difference between vector addition and algebraic addition. Algebraic Addition applies to vectors and scalars: [a ,A ] + [b, B] = [a+b, A + B]. Algebraic addition handles the scalars a and b the same as the Vectors A and B


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