Question

Let r= be an arbitrary vector. In each part, describe the set of all points (x,y) in 2-space that satisfy the stated condition.

Answer 1

\[\left| \left| r \right| \right|\le1\]

Answer 2

isn't that simply the unit circle

Answer 3

How would you do this problem? im stuck

Answer 4

those are the points equidistant from a fixed origin

Answer 5

are they outside the radius or inside?

Answer 6

inside

Answer 7

yes inside

Answer 8

oh because its less than? oh right. duh

Answer 9

im having dumb shocks atm

Answer 10

less than or equal!
if it is just than that would be another story i think

Answer 11

does this apply in 3-D aswell?

Answer 12

well if the origin is fixed you would get a sphere! but if the origin is chosen at random
you have something rather different

Answer 13

i was trying to picture this but sucks not good enough at \(R^3\)

Answer 14

@SithsAndGiggles

Answer 15

ahh

Answer 16

perhaps siths will give us a nice interpretation here^_^

Answer 17

alright, ima do my longass calc hw and look up from time to time at my comp screen

Answer 18

this is calc?

Answer 19

isnt it not? im taking calculus 3 rn

Answer 20

is*

Answer 21

yes should be^_^

Answer 22

\[\|r\|=\sqrt{x^2+y^2}\]
If \(r=1\) (at most), then you have the circle with radius 1 centered at the origin.

For any value of \(r\) less than 1 (but obviously greater than 0), the vector will occupy all points *inside* the circle.

So you have all the points on the boundary of the circle as well as the points surrounded by the circle. This region is called a disk (centered at (0,0) with radius 1).

Answer 23

so this would apply in 3d realm except it would just be occupying inside, outside, and on the sphere?

Answer 24

let me ask you this question! does the center have to be at (0,0) since it said arbitrary vector?

Answer 25

logically, arbitrary vector can be anywhere, but i think they meant to start at the origin becuase it involves 1. iono whenever i see 1 after taking trig, i think of the unit circle

Answer 26

i typed out the question exactly how its worded in the textbook.

Answer 27

well we could have a circle with radius at any given center
we would still get the circle as long as the center is a fixed point?

Answer 28

radius 1*