You want to find the dot product between two vectors, \(\vec{A}\) and \(\vec{B}\text{.}\) What do you know about the directions of vectors if the dot product is positive? What if the dot product is negative? What if the dot product is zero?
The area vector \(\vec{A}\) for a surface points perpendicular to the surface, with a magnitude equal to the area of the surface. For an infinitesimal surface, the area vector is typically written \(d\vec{A}\text{.}\) An area vectors has units of \(\mathrm{m}^2\)
Write a differential area vector \(d\vec{A}\) for a small part of the front cover of the book in terms of differential elements like \(dx\) and \(dy\text{.}\) Check that your expression has the correct units!
