What do you do with a vector? First thing, you add them, vectorially. And then? ....simple! you multiply them.....and then you realise there are actually two ways to do so! One is scalar product, while the other is vector product.
This is the way a typical 12th standard class goes in. I always wondered, why the hell are there two ways? From where did they come from? What was the clue?......Even after a laborious work at length, I couldn't get a clue.
It was only when the introduction to tensor came in my way, I realised that the vector product is indeed not a simple vector. It is dual of some anti..........blah blah!
The actual point I learned was " The direction of the vector, the (vector) product of two vectors, is merely a convention"......consequence of what is called as right handed co-ordinate system.
And we are so used to it.......when you twist the screw in the wall, when you close the running water tap and also when you open your medicine bottle or even when you key your watch! Its all right handed systems.
As far as you are a physicists or an engineer it is just logical. But what if you are a biologists?
Consider, a long flat sheet hold it at one end with your left hand and start twisting with your right hand the most natural way (i.e. clockwise). The thing which you get is a right handed spiral, a model for a right handed DNA in biology. But, have a closer look at it and you will realise, that it is a left handed screw one according to the physiscists' definition.
Amazing realisation! isn't it?
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5 comments:
Your post reminds of the all the stuff that I ought to remember but have forgotten *sheepish grin*. That is an intereting observation that a right handed DNA is a left handed screw. But I dont understand how the vector direction and the right handed co-ordinate system link up.
Actually, a cross product is not a process of multiplication. I don't want to bore you with physics fundae, but briefly, it is what is called "a second rank totally anisymmetric tensor" and under very special cases it looks like a vector. Though the direction is not well defined.
And here comes the convention of co-ordinate system. We have adopted a system such that x cross y = z and not -z
Another experiment: look into mirror and lift your left hand, you will see that your image is lifting its right hand ;)
I would say evrything is "right" in this world!
a second rank totally anisymmetric tensor
Yup! That makes perfect sense. Thanks.
Amit
This is a nice observation. Actually, many a times I get confused with the razor I must incline to my face, while shaving, for proper cut....it is very tough deciding while looking into the mirror
Smudrika
It must read "antisymmetric"! I emptied my "tea" there!
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