Cartesian Definition and 549 Threads

Okay, I was doing 3D modelling. To save space I used vector functions to render terrain. Anyway, I came up with 3 parametric equations - each a function of an axis: e.g.: x=4t, y=5t+6, z=7t-9. How can you convert this into a Cartesian Equation?:confused:

Source: Halmos, Naive Set Theory I ran into a bit of confusion in the way Halmos generalizes the "Cartesian Product" for a family of sets (p.36). I was wondering if someone can shed some light on this. Here is my problem: Previously, Halmos defines the cartesian product of two sets X...

Hi all... Homework Statement Let A, B be non-empty sets, proof that A x B = B x A iff A = B Homework Equations A x B = Cartesian Product iff = if and only if ^ = and The Attempt at a Solution Let (x,y) є A x B = B x A iff (x,y) є (A X B) ^ (x,y) є (B x A)...

What is the sequence described by the counts of integer Cartesian coordinates (x, y) within circles of successive whole number radii centered at the origin?

Homework Statement find polar coordinates of the points whose cartesian coordinates are given. Homework Equations heres the point: (3sqrt(3), 3) The Attempt at a Solution well i know that r^2 = (sqrt(a^2 + b^2)) so the answer here is : 6 and if we use tan(theta) = o/a =...

Homework Statement See attachment, I am getting everyone of these problems wrong. Homework Equations M_y = u_y(r_y X F) Where u=unit vector defining the direction of y axis r=distance from y-axis to any point on the line of action of F F=acting force...

Does the plane that intersects the cone need to be parallell to the axis of the cone to make the section a hyperbola, or is it enough that it is not parallell to a generator? If the latter is correct, can one say that a parabola is a special case of a hyperbola?

I don't know where have I gone wrong... I converted Cartesian coordinates to polar coordinates: \frac{\partial^2\Psi}{\partial x^2} +\frac{\partial^2\Psi}{\partial y^2}= \frac{1}{2}(\frac{\partial^2}{\partial x^2}+\frac{\partial^2 }{\partial y^2})\Psi^2 - \Psi(\frac{\partial^2}{\partial...

I have a question relating to a particle rotating around a point with velocity u = \Omega \times r, where \Omega is the angular velocity and r is the position relative to the pivot point. I need to prove that the acceleration is given by, a = -\frac{1}{2} \nabla [(\Omega \times r)^2] I...

ok I am give a parametric equations of x= 4 cos t and y=5 sin t I know that i have to solve the x equation for t then stick it in the y equation but i getting stuck or not rembering some simple stuff i should be. I believe i get t= cos(inv) (x/4) and substiute it into t in y. if so...

I have no idea how to do this. I've tried a lot of things but I can never reduce it to solely cartesian coordinates. Is there any hard fast procedure to conversions like this? thanks.

With the success of my effort to write the orbits of the Schwarzschild metric in "Cartesian" coordinates, (see https://www.physicsforums.com/showthread.php?t=126996 ) it is now time to compute the orbits for Painleve coordinates. When I'm done, I will have an applet that allows the computation...

Hello everyone. I read in a book that for metric spaces (X, \rho), (Y, \sigma) we can form the metric space (X \times Y, \tau_p) , for 1 \leq p < \infty where \tau_p is given by: \tau_p((x_1,y_1), (x_2,y_2)) = (\rho(x_1,x_2)^p + \sigma(y_1,y_2)^p)^\frac{1}{p} I can easily verify the...

I have no clue where to start on this question. Use Cartesian vectors in two-space to prove that the line segments joining midpoints of the consecutive sides of a quadrilateral form a parallelogram. Atm all i can deduce from the information is that vectors 2A+2B+2C+2D=0 therefore midpoint...

Hello Im working on some line integral problems at the moment. The first one is really only a check - I think I've worked it out... Compute the line integral of the vector field B(r) = x^2 e(sub 1) + y^2 e(sub 2) along a straight line from the origin to the point e(sub 1) + 2 e(sub 2) + 4...

Hello, are all Oval Shaped Cartesian Curves" +/-(x^2) " or we can have it with other degrees??

My Java applet gravity simulator http://www.gaugegravity.com/testapplet/SweetGravity.html draws beautiful orbits, however the GR simulation is very badly broken as one can tell when comparing it with Newton at long distances. The source code is at...

This is driving me crazy, I just can't see how to do it. I want to express the cartesian unit vectors \hat{x}, \hat{y} and \hat{z} in terms of the spherical unit vectors \hat{r}, \hat{\theta} and \hat{\phi}. I have tried to do something similar in polar coordinates (just to make it a bit simpler...

Hello. I am interested in learning the mathematical derivation from Cartesian coordinates Navier-Stokes equation to cylindrical coordinates Navier-Stokes equation. These equations have similar forms to the basic heat and mass transfer differential governing equations. I’ve tried looking...

Hey everyone, my lecture has given me this question, I am unsure where to start with it. Express the Cartesian point (3, 3) in polar coordinates. Do i need to use the sin and cos on my calc. Any help would be very helpful lakitu

Has anyone ever done an experiment called "The Cartesian Diver"? The instructions are below, just in case...:smile: 1. The medicine dropper is the "diver" which will be put into the water. 2. Fill the graduated cylinder with water to about an inch from the top. 3. Fill the...

how convert dis to cartesian form!? quation was here and then i will need to sketch on an argand diagram. help apreciated thnx

Find the Cartesian equation of each of the following lines. (x,y)=(4,-6) + t(8,2) Not sure how to do it, I know that you need the normal which is (-2,8) I've tried a lot of times and I don't get it

i have this equation: r=\sqrt{1+sin2\theta} and am to convert to cartesian equation and from the equation see that it consists of two circles and directly note the radii of the cirlcles from the equation. so far i have manipulated it and gotten: x^6 + 3x^4 y^2 + 3 x^2 y^4 + y^6 - x^4...

How to get the Cartesian coordinates of an atom? Dear friends, Such a question confused me when reading!:confused: "xi,yi and zi are the Cartesian coordinates of the ith atom" How to get the coordinate of an atom? For example: carbon, oxygen? I think the atom is only a dot! What's the way...

Hmm, I can't seem to get this double integral transformation: int(limits of integration are 0 to 3) int (limits of int are 0 to x) of (dy dx)/(x^2 + y^2)^(1/2) and i need to switch it to polar coordinates and then evaluate the polar double integral. i sketched the region over which i am...

i would like to know how a cartesian diver works using mathematics. I have found how the diver works using words and explanation but not using equations and math. Please HELP!

Given the typical cartesian xyz- coordinate system, is it correct to speak of a position vector? Isn't (x,y, z) just shothand for the coordinates? Distance vectors, force, velocity are real vectors with magnitude and direction in position space, but what is with a position vector in position...

(1)If you are given the parametric equations x = sin(2\pi\t) y = cos(2\pi\t) and 0\leq t\leq 1 how would you find the cartesian equation for a curve that contains the parametrized curve? Using the identity \sin^{2}\theta + cos^{2}\theta = 1 would it be x^{2} + y^{2} = 1 ? Thanks

I'm back studying after a couple of years out and have become a little rusty. currently learning about the J operator. I have no problem converting Cartesian to Polar, but struggle to convert Polar to Cartesian. Some basic examples and a step by step guide would be appreciated. Thank...

Is it true that \mathbb{R}\times \mathbb{R}^2 = \mathbb{R}^2 \times \mathbb{R} = \mathbb{R}^3 ?

What is the difference in the "uniqueness" of the representations of Cartesian coordinates and in polar coordinates? :confused: Also, what is the non-uniqueness?

These are just a few questions that a don't understand and any help would be great. 1. Prove that the line (x-3)/2 = (y-4)/3 = (z-5)/4 is parallel to the plat 4x + 4y - 5z = 14 2. Find the equation of the line through (1,0,-2) and perpendicular to the plane 3x - 4y + z -6 = 0...

Hi everybody, When we have two sets A and B , we define the cartesian product of A and B as the set A*B={(x,y): (x element of A) and (y element of B)}. We also define A*A*...*A (n factors)=A^n. So when we write (A^2)*B, this is the same as A*A*B? I mean, for example (R^2)*R is the same as...

Is there any law for finding the root of a complex number in catesian coordinates? without changing to polar, I've created 1, i just want to know is it worthy or not, so ... everybody who reads the message, please post the ROOT OF A COMPLEX NUMBER IN CARTESIAN COORDINATES LAW and let me...

This section I don't understand at all... but the problem is What is the torque tau_B due to force F_vec about the point B? (B is the point at Cartesian coordinates (0, b), located a distance b from the origin along the y axis.) Express the torque about point B in terms of F, theta, phi, pi...

I find this passage \frac{\partial}{\partial x} = \cos(\phi)\frac{\partial}{\partial \rho } - \frac{\sin(\phi)}{\rho}\frac{\partial}{\partial \phi} difficult to understand. My teacher wrote this as an explanation: \frac{\partial V}{\partial x} = \frac{\partial\rho}{\partial...

Are Cartesian coordinates two or three dimensional?

What are the differences in the "uniqueness" of the representations in Cartesian coordinates and in polar coordinates?

Find a cartesian equation for the perpendicular bisector of the line joining: A, (2,3) and B, (0,6). Haven't come across this before, and really am stuck! Thanks in advance.

Just got back into physics after 4 years in social science and I have forgotten how to convert cartesian coordinates to polar coordinates. The textbook I have makes no metion of it. probably bc I am expected to know this, but I can't remember. I remember how to calculate the distace between two...

I've no idea what to do with this, the examples didn't have anything of this style: The point A has coordinates (3,0,0), the point B has coordinates, (0,3,0), the point C has coordinates (0,0,7). Find, to 0.1 degrees, the sizes of the angle between the planes OAB and ABC, where O is the...

Using converse of alternate segment theorem (i think it is) i.e. this: "If the line joining two points A and B subtends equal magnitude angles at two other points on the same side of it, then the four points lie on a circle" establish the cartesian equation, range and domain of the locus...

I am struggeling with the following problem: give the x,y,z coordinates from the following ball points/vectors 1. (r, theta, phi) = (sqrt3, 3/4pi, 3/4pi) 2. (r, theta, phi) = (1, 1/6pi, 1 1/6pi) the sollutions I found in my reader are as followed: 1. (x, y, z) = (-1/2 sqrt3, 1/2...

Just to make sure I got this right. Cartesian is the popular x,y,z. Polar is the one with degrees, and has a circular shape. Is that it?

Does anyone have a quick method to do this?

Hi. I was just wondering if anyone could help me with a formula to solve the following problem. I have two locations (L1 and L2), which I know the cartesian coordinates of, situated in a three dimensional space. I also have a distance (D) which I also know the value of. D is not the...

if R = sinti+sqrt(2)costj+sintk, 0<=t<=Pi/2 please eliminate t to determine the cartesian equation of R(t). Put limits on the variables and verbally describe the curve

Well, it is not really hard to convert them. My main problem is thinking in Polar coordinates. Cartesian coordinates are really easy to think about for me (after how many years of experience) but then I get to Calc 3 and I hit a brick wall. Does anyone have some insight on how to get past...