**1**,

**2**]

\[ \begin{align} \mathbf{A} \cdot \mathbf{B} &= \left(A_1 \mathbf{e}_1 + A_2 \mathbf{e}_2 + A_3 \mathbf{e}_3 \right) \cdot \left(B_1 \mathbf{e}_1 + B_2 \mathbf{e}_2 + B_3 \mathbf{e}_3 \right) \\ &= A_1 B_1 + A_2 B_2 + A_3 B_3 \end{align} \]

That is, the dot product multiplies each corresponding component of the vectors and adds them together to obtain a scalar. So you could also call this a vector component product.

In progress...to be continued.

**References:**

[

[

**1**] K. Karamcheti. Principles of Ideal-Fluid Aerodynamics. John Wiley & Sons, Inc., New York, NY. 1966[

**2**] W. Kaplan. Advanced Calculus (5th ed.). Addison-Wesley. 2002
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