Orientation of Vector3.forward

I want to use…

Vector3.up;
Vector3.left;
Vecotr3.forward;
...

to translate my camera’s position, but the camera could be facing any direction,

eg.

  (mycamera.directionOfView - defaultStartingDirectionOfView) == differnceFromDefault
  newDirection == differenceFromDefault * Vector3.up;
then
  camera.transform.Translate(newDirection * (velocity), Space.World);

My maths is lacking a bit so I dont have the terminology to properly explain, so feel free to use big maths words I can google later.

Vector3.forward
Vector3.right
Vector3.up

are always directions relative to the “world”. They are the same for every object, whichever way they are facing. (Note that there is no Vector3.left - that’s just -Vector3.right).

If you want to know local directions relative to a particular object’s current rotation, use the properties of that object’s transform component:

transform.forward
transform.right 
transform.up