Calculus
Prove each property using Cartesian vectors:
A) (u +v) + w = u + (v + w)
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Answers
Proof. This property can be proven using Cartesian vectors. Using the definition of vectors, u=(u1, u2, ..un), v=(v1, v2, ..vn), and w=(w1, w2, ..wn), we can prove that: (u+v)+w = (u1+v1)+w1, (u2+v2)+w2, .. , (un+vn)+wn and u+(v+w) = u1+(v1+w1), u2+(v2+w2), .., un+(vn+wn) Comparing these two equations, it is seen that they are the same, so (u+v)+w = u+(v+w) is true.
