Is a point "P" on a plane considered a zero vector, PP, or is there a difference between a single point and a zero vector?

Can there be a polar representation of a single point? If so, would it be <0> ?

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- Feb 21st 2008, 05:14 AMbillymproperties of the zero vector
Is a point "P" on a plane considered a zero vector, PP, or is there a difference between a single point and a zero vector?

Can there be a polar representation of a single point? If so, would it be <0> ? - Feb 21st 2008, 08:15 AMSoroban
Hello, billym!

Interesting . . . "Zero" always raises strange questions.

Quote:

Is a point $\displaystyle P$ on a plane considered a zero vector, $\displaystyle \overrightarrow{PP}$

or is there a difference between a single point and a zero vector?

__always__a difference between a point and a vector.

The point might be $\displaystyle (2,3)$ and the zero vector is: .$\displaystyle \langle 0,0\rangle$

Quote:

Can there be a polar representation of a single point?

If so, would it be $\displaystyle \langle 0\rangle$ ?

*pole*(origin), the polar coordinates are: .$\displaystyle (0,\theta)$

. . where the 'magnitude' is 0 $\displaystyle (r=0)$ and $\displaystyle \theta$ can be any angle.

Other points have coordinates such as: .$\displaystyle \left(2,\,\frac{\pi}{6}\right)$

- Feb 21st 2008, 09:06 AMbillym
I'm still confused... what would be the polar representation of of a point with coordinates (-3,4)?

- Feb 21st 2008, 09:12 AMbobak
- Feb 21st 2008, 09:23 AMbillym
In terms of direction, do you treat the point as if it were a position vector, and then just state the magnitude as zero?

- Feb 21st 2008, 09:35 AMPlato
It would be quite fair if someone argued that yours is a philosophical rather than a mathematical question.

*Vectors*are hybrid objects in that*a vector has both length and direction*.

Here is a quotation from Melvin Hausner, a geometer at NYU, “The vector $\displaystyle \overrightarrow {PP} $ will be designated by(read: zero, or the zero vector, depending on how fussy you are.) Thus $\displaystyle \overrightarrow {PA} = 0$ is a way of writing $\displaystyle P = A$.”**0**

To answer your other question: $\displaystyle \left( { - 3,4} \right) \equiv \left( {5,\pi + \arctan \left( {\frac{{ - 4}}{3}} \right)} \right)$. - Feb 21st 2008, 09:55 AMbillym
but I'm trying to find the polar representation of just a point (-3,4), how could a point have magnitude of 5?

- Feb 21st 2008, 10:15 AMbobak
Spend some time reading this, Polar coordinate system - Wikipedia, the free encyclopedia