The property:

In terms of unit vectors, if $a =\begin{array}{l}a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{k}\end{array}$

and $\begin{array}{l} b = b_1 \hat{i} + b_2 \hat{j} + b_3 \hat{k} \end{array}$ then,

\begin{array}{l}a.b = (a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{k}).(b_1 \hat{i} + b_2 \hat{j} + b_3 \hat{k})\Rightarrow a_1b_1 + a_2b_2 + a_3b_3\end{array}

In terms of unit vectors, if $a =\begin{array}{l}a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{k}\end{array}$

and $\begin{array}{l} b = b_1 \hat{i} + b_2 \hat{j} + b_3 \hat{k} \end{array}$ then,

\begin{array}{l}a.b = (a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{k}).(b_1 \hat{i} + b_2 \hat{j} + b_3 \hat{k})\Rightarrow a_1b_1 + a_2b_2 + a_3b_3\end{array}