New Directions in Vectors

Vectors! snorted Pliny. I need no introduction to the topic of vectors. Vector is a Latin word. We Romans invented vectors. Without them we could not have built our famous aqueducts.

Oh, sorry, Pliny. I hadn't thought of that. That's lucky really, because I was never any good at vectors. In fact, when I studied vectors in Physics, at school, I only learned one thing about them.

And what was that? asked Pliny.

It was that you can use them to work out something about a horse pulling a barge down a canal. And that you do it by drawing a triangle with arrows. And that no matter how long you look at that triangle, and no matter what answer you come up with, the answer is always the opposite.

The opposite of what? asked Pliny, looking a little vexed.

Exactly! I said. The opposite of what? I don't think I ever got one right.

You shouldn't have given up, said Pliny. It sounds to me as though you were on the right track. If you knew that the answer was always the opposite, all you had to do was give the opposite answer to what you had come up with.

Yes, but Pliny, you always had to show your working out.

That need not have been a problem. Having completed the working out, you would only need to write it out again, but in reverse.

Gosh, Pliny, I see why you Romans were so good at using vectors.

Indeed. Romans have always been practical people.