PX275 - F2 - summation conventions

\vec{a} = a_{x} \hat{i} + a_{y} \hat{j} + a_{z} \hat{k} = \sum_{i = 1}^{3} a_{i} x_{i}

where, $x_{1} = \hat{i}$ , $a_{1} = a_{x}$ , and so on

\vec{a} = a_{i} x_{i}

\vec{a} = a_{i} x_{i}; \vec{b} = b_{j} x_{j}

\vec{a} \cdot \vec{b} = a_{x} b_{x} + a_{y} b_{y} + a_{z} b_{z} = δ_{i j} a_{i} b_{j}

where, the kronecker delta, $δ_{i j} = {\begin{cases} 1 & if i = j \\ 0 & if i \neq j \end{cases}$