The average tornado has forward speed of 30mph. Some reach speeds of 70 mph but not very many do that. How long does it take you to drive perpendicular to a tornado 2 miles wide at 60mph when you are driving at approximately right angles to the tornado?
And BTW I have seen what happens to a trailer park in the track of an average tornado up close and personal about 35 years ago. Not a chance in hell I would stay in a trailer with a tornado tracking my way when the truck is in the driveway.
Smart people who live in tornado alley, especially in towns that have been hit, have a storm cellar.
To answer that, download the Radar Navigation and Maneuvering Board Manual. Go to page 258 (Chapter 6), Course at specified speed to pass another ship at maximum and minimum distances, which is also applicable to tropical storms.
You can see there that the course you want to take is dependent on the vectors and magnitude of your car and the tornado, and that it's not a right angle. In the example provided there, where the other ship has a course of 300 degrees, neither your own maximum distance by taking a course of 000 (=360) degrees nor your minimum distance by taking 240 degrees approximate a right angle (30 and 210) from a storm.
Remember that if you take a right angle (a) from a storm's path, it's closest point to you, when it passes, will lie at the intersection of your path and its own (A; plot your line in the other direction). But if you're driving at an angle (b) that keeps you ahead of the storm's path while heading away from it, when that storm reaches point A, you're still ahead of the storm and can still drive further before it reaches closest point of approach B.
I don't know if that direction is normally 60 degrees from the storm's course or if it just happened that way in the example they gave on the maneuvering board. I haven't practiced any of these in real life and just know about the maneuvering board because I was looking things up for a roleplaying game.