[Physics] Difference between negative and positive sign before a scalar and a vector quantity

notationvectors

What is the difference between use of signs('-' and '+') before a vector and a scalar quantity?
For example,we can use '-' or '+' sign before Displacement which is a vector quantity and we can also use '-' or '+' sign before Joule which is a scalar quantity.
So,what is the difference between the use of signs before vectors and scalars?

Best Answer

I don't think this question really has a general answer so I will give a few physics examples from which you can draw conclusions as you wish:

Scalar

  • Electric charge or spins in the Ising model: Here the sign affects the type of the "particle/spin/...". A positive charge will be attracted to a negative charge while being repulsed from a positive charge. Similarly spins of like signs will interact differently in the Ising model to spins of opposite signs.
  • For quantities like energy,... or others that are essentially defined as a difference between two states, the sign can indicate whether the quantity is consumed or accumulates.
  • In some (few) cases a quantity can have positive and negative values without any deeper meaning. This is the case for temperature measured in Celsius or Fahrenheit.

Vector

With vectors, the sign determines the direction. If you change only the sign of a vector, you essentially have it point in the opposite direction. This is true for all kinds of vectors you encounter such as a force changing direction, velocity (moving in opposite direction,...

Related Question