I am attempting to slow down the speed of all entities within a specific range of the player.  The method I am doing this is working, but is resulting in odd behavior (like arrows stopping suddenly in air and then rapidly updating their position, mobs visually oscillating, etc).  Here is my current method:

 

List<Entity> entitiesToSlow = world.getEntitiesWithinAABB(Entity.class, AxisAlignedBB.getBoundingBox(player.posX - 5, player.posY - 5, player.posZ - 5, player.posX + 5, player.posY + 5, player.posZ + 5));
			if(entitiesToSlow.size() > 0)
			{
				for(int i = 0; i < entitiesToSlow.size(); i++)
				{
					Entity e = entitiesToSlow.get(i);
					if(e instanceof EntityPlayer)
					{

					}
					else
					{
						double velx = (e.posX - e.prevPosX);
						double vely = (e.posY - e.prevPosY);
						double velz = (e.posZ - e.prevPosZ);

						if(velx != e.getEntityData().getDouble("slowX") || vely != e.getEntityData().getDouble("slowY") || velz != e.getEntityData().getDouble("slowZ"))
						{
							e.getEntityData().setBoolean("inSlowZone", false);
						}
						if(!e.getEntityData().getBoolean("inSlowZone") )
						{ 	
							double factor = 0.7D;

							e.setVelocity(velx * factor, vely * factor, velz * factor);
							e.getEntityData().setBoolean("inSlowZone", true);
							e.getEntityData().setDouble("slowX", velx * factor);
							e.getEntityData().setDouble("slowY", vely * factor);
							e.getEntityData().setDouble("slowZ", velz * factor);
						}
					}
				}

 

Is this the best way of slowing down the speed of an entity by a specific factor if it's within a specific area of the player? 

I cannot say what is the best way to slow entities (like within a ring of frost), but I can tell you that you do not want to use dot-product on a velocity vector.  You only want to save the magnitude by a specific amount. The magnitude of a velocity is sqrt(vx^2 + vy^2 + vz^2), scale that magnitude by .7 or whatever, then multiply it by the velocity unit vector to get the proper adjusted speed.

You could use ((EntityLivingBase)entity).addPotionEffect(new PotionEffect(2, 200, 1));

Adding a potion effect will not work for me, as I need this to affect ALL entities, not just living entities.