Starting from the definition of the position vector of the center of mass, show that ∑k=1^n mk(𝐫

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Step 1:u000ALetu0027s start with the definition of the position vector of the center of mass. For a syst

Starting from the definition of the position vector of the center of mass, show that $$ \sum_{k=1}^n m_k\left(\mathbf{r}_k-\mathbf{r}\right)=\mathbf{0}, \quad \sum_{k=1}^n m_k\left(\mathbf{v}_k-\mathbf{v}\right)=\mathbf{0} $$ Where were these identities used?