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edited title and added appropriate "vector"-tag

How to avoid `Times[OverVector[F],0]` to be evaluated as 0?

I am fairly new in Mathematica and I am trying to work with scalars and vectors. I decided to denote vectors using OverVector (as example, OverVector[F]stands for the force). Any scalar is denoted by a symbol.

When an expression has a multiplication between scalar and vector, the expected outcome should be nullVector, but Mathematica evaluated this as zero. (I have been using Notation package and Notation[OverVector[0]\[DoubleLongLeftRightArrow]nullVector], nullVector stands for the zero vector)

How I can prevent Mathematica to evaluate Times[OverVector[F],0] as zero?

In other words. I need Mathematica evaluates the multiplication between vector and zero as the zero vector (nullVector) not as zero. How I can get this?

Thank you so much.