Question

Does vector addition satisfy the associative law of addition?

Answer 1

Vector addition satisfies the associative law for addition, meaning that when we add three vectors, say $\mathbf{u}, \mathbf{v}$, and $\mathbf{w}$, it does not matter which two we add first; that is, $$ \mathbf{u}+(\mathbf{v}+\mathbf{w})=(\mathbf{u}+\mathbf{v})+\mathbf{w} $$ It follows from this that there is no ambiguity in the expression $\mathbf{u}+\mathbf{v}+\mathbf{w}$ because the same result is obtained no matter how the vectors are grouped.