Math Is Fun Forum

glenn101

Member

Registered: 2008-04-02

Posts: 108

Why is it that {R:r=1} where R is a position vector resembles a circle

The position vector meaning the tail of the vector is at the origin. And this is in R^2 with plane polar coordinates.

I thought that the sketch of this set would resemble a set of position vectors with magnitude 1 extending out to a radius of 1 which trace out to reach a point which would lie on a circle of radius 1, but because of the lengths of each of the position vectors, wouldn't the region be a filled in circle(a disc)? Why do we neglect the lengths?

Any help would be much appreciated, this idea has confused me for a while.

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"If your going through hell, keep going."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Why is it that {R:r=1} where R is a position vector resembles a circle

hi glenn101

r = 1 just means the point at the end of the vector, so only the circumference, not the disc.

A position vector tells you the position of a point.  You start at the origin and travel the vector but what you end up with is just the point.

To generate the inside of the circle the definition would read r ≤ 1

Bob

Last edited by Bob (2011-05-16 19:41:33)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

glenn101

Member

Registered: 2008-04-02

Posts: 108

Re: Why is it that {R:r=1} where R is a position vector resembles a circle

Thanks so much for the reply Bob,
So if we had {R:r<=1}
We would have position vectors where the end of each vector resembles a point inside the circle?

i.e. the lengths don't count as points only the ends of the vectors give us points?

---

"If your going through hell, keep going."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Why is it that {R:r=1} where R is a position vector resembles a circle

Yup;  that's what I think.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob