Dot Product vs Cross Product

Introduction

DOT product and Cross product are important to quantify 3-D geometric depended relationship of electrical circuit effects.

Overview

DOT product: output is the multiplicative product of effective parallel components of two vectors.

• Example vectors can be voltage waves along a transmission path such as straight copper trace. When the wave is propagate perfectly along the transmission path. We can predict the wave magnitude along each x position of the transmission by dot product the wave function and the distance function.

Cross product: output is the is the multiplicative product of effective perpendicular components of two vectors.

• Example: Lorentz force
  • Two vector quantities are the current (I) guided by a wire (L) and the magnetic field (B) produced by a strong magnet.
    • Note: a vector contains both a magnitude and direction, in the above case current is the magnitude and direction is guided by wire.
  • Resultant force on the current carrying wire is the Cross product of current vector and magnetic field vector
    • F= I*L X B