10.4: Matrix Formulation
( \newcommand{\kernel}{\mathrm{null}\,}\)
The dot product can also be written in matrix form. To begin, let's represent vectors as column vectors-that is, 3×1 matrices. We'll define the vectors A and B as the column vectors
A=(AxAyAz);B=(BxByBz)
The dot product can then be written
A⋅B=ATB=(AxAyAz)(BxByBz)=(AxBx+AyBy+AzBz).
This the the product of a 1×3 row array with a 3×1 column array, which gives a 1×1 result (i.e. a scalar).