Question

Can a vector have a magnitude less than zero? :D

Answer 1

When you derive the equation for potential due to point charge. We calculate the following integral


Now the work doen by the force is

\[W = \int\limits_{\infty}^{p}F.dx = -\int\limits_{\infty}^{P}Fdx\]

The integral is a dot product of force and dx
clearly both are in the same direction
so what is the source of that negative sign


It is often mentioned that dx is negative, because it is going against the increasing direction
so i was wondering can vector have a magnitude which is negative number?