Which is the grammatically correct statement :
"We are travelling in a car"
Or
"We are travelling by a car"
Which is the grammatically correct statement :
"We are travelling in a car"
Or
"We are travelling by a car"
If you say travel by something, it means you are travelling by the means of transportation. For example, "I travelled by car" means that I am travelling using a car for transportation.
If you say travel in something, it means you are literally travelling while inside a specific vehicle. For example, "I travelled in a car" means that you are travelling literally inside a car.
Another smaller nuance is that in America (US) we spell it "traveling". Don't know if the question was about British usage or American.