I Why we use vectors?

1. Mar 15, 2017

Ahmed Elhossiny

Hello there,
get the notion of position vectors for a particle, but why we use it instead of cartisean coordinates XYZ? What info does the vectors tell us that the cartisean coordinates doesn't tell us?
So if we say a point has coordinates x=2, y=3, z=5

We say its position vector is
r=i 2 + j 3 + k 5

What's the difference!! I saw an article saying it's just another way of expressing the position

2. Mar 15, 2017

pixel

Yes, either form in your example has the same information. But an equation written in vector form is independent of any particular coordinate system. That makes them useful for expressing the laws of physics.

3. Mar 15, 2017

Ahmed Elhossiny

Doesn't it depend on the X,Y and Z unit vectors? Even if I chose another coordinate system I should express it in terms of the first by (phi)?

4. Mar 15, 2017

pixel

You can always transform coordinates to get back to x, y and z. But in some cases, other coordinates are more natural, simpler and useful to apply.

5. Mar 15, 2017

Staff: Mentor

The Cartesian coordinates of a vector is just one possible of infinitely many possibilities to express a vector according to a basis. But what if you consider the functions? They, too, form vector spaces. Or sequences? The concept of vectors simply restricts the view and methods to what is really needed: addition and stretching (compressing) without the need of one single basis to be used.

6. Mar 15, 2017

Ahmed Elhossiny

And that's not applicable in XYZ expression! That's why it's more useful

I always thought it has something to do with direction of movement :D turns out I am wrong

Thanks

7. Mar 15, 2017

Ahmed Elhossiny

Can you give me an example of how to express same vector in two cartisean coordinates expression?

8. Mar 15, 2017

Staff: Mentor

The easiest way is to renumber the coordinates: $(0,1)$ in one coordinate system can be $(1,0)$ in another. Without telling everybody which orientation you use, it is of little help. But you could still say vertical or horizontal unit vector. And why Cartesian coordinates? Sometimes polar coordinates are far easier to handle. And you will have problems to define Cartesian coordinates on the space of all smooth functions on, say a sphere.

9. Mar 15, 2017

Arman777

Vector's are needed mathematical concepts in physics I think (so in expressing nature).I mean it cant just be some coordinate transformation simplicty.

Think Force or even simpler case, velocity.If velocity would be just scaler, things would be very hard to express.The direction comes naturally these things.And of course we need a magnitude so simply we need a vector.You need vectors to desribe nature correctly.You have a displacement "vector" cause it describes the direction and also magnitude.Lets take a object at point (3,4,5).If you had just this info you cant tell which direction you are, maybe you come from (1,8,9) maybe ( 2,3,4).So a vector can describe the motion of a particle which thats why we use displacement "vector",then from there velocity etc.