Dot Product vs Cross Product

Introduction

The concepts of DOT product and Cross product are essential in quantifying the 3-D geometric relationships that influence electrical circuit effects.

Dot product

The DOT product produces an output that represents the multiplicative product of the effective parallel components of two vectors. For example, when considering voltage waves along a transmission path, such as a straight copper trace, the DOT product allows us to predict the wave magnitude at different positions along the transmission by multiplying the wave function with the distance function.

Cross product

The Cross product, on the other hand, yields the multiplicative product of the effective perpendicular components of two vectors. For instance, consider the case of Lorentz force. Two vector quantities involved are the current (I) flowing through a wire (L) and the magnetic field (B) generated by a strong magnet. In this scenario, the current represents the magnitude, and the wire guides its direction. The resultant force acting on the current-carrying wire can be calculated using the Cross product of the current vector and the magnetic field vector:

F = I * L x B

It is important to note that a vector encompasses both magnitude and direction. In the example mentioned above, the current represents the magnitude, while the wire guides its direction.

Summary

By utilizing the DOT and Cross product operations, we can effectively analyze and understand the intricate relationships that govern various electrical circuit phenomena in three-dimensional space.