Cartesian Definition and 561 Threads

Hi, I want to calculate the potential energy between two opposite charges (a dipole) and I know how to integrate Coulomb’s law in the polar form, i.e. in terms of “r” \[...

I have a question that I am trying to find proof and/or references for: Suppose we have two sets of points (P1 and P2) in separate N-dimensional Cartesian Spaces S1 and S2. *** Note: if it can be easily extended to the Euclidean Space - even better. We need to find Affine Transformation...

Hi, I would like to transform a vector from Spherical to cartesian coordinate system. But the question is probably not that straight forward. :( I have a vector say E = E_r~\hat{r}+E_{\theta}~\hat{\theta}+E_{\phi}~\hat{\phi}. But I know only the cartesian coordinate from where it...

We had to do a lab on the cartesian diver and there were a few questions that I was unsure on. Here they are: What are some possible modifications to the diver that would cause it to sink quicker or slower? What would happen if the bottle was only half full of water or there was no cap...

Homework Statement The general equation of motion of a non-relativistic particle of mass m and charge q when it is placed in a region where there is a magnetic field B and an electric field E is m\bold{\ddot{r}} = q(\bold{E} + \bold{\dot{r}} \times \bold{B}) where r is the position of...

I am not able to find good books on this topic on net so if any 1 can help me i will be grateful .

Homework Statement Show using cartesian components that d/dt(a.b)=(da/dt).b+a.(da/dt) The Attempt at a Solution a= axi+ayj+azk b=bxi+byj+bzk a.b=axbx+ayby+azbz d/dt(a.b)= d/dt(axbx+ayby+azbz)

Homework Statement This is my last question about triple integrals in cylindrical coordinates. Evaluate the integral by changing to cylindrical coordinates: \int _{-3}^3\int _0^{\sqrt{9-x^2}}\int _0^{9-x^2-y^2}\sqrt{x^2+y^2}dzdydx Homework Equations In cylindrical coordinates...

Homework Statement Use a triple integral to find the volume of the solid enclosed by the paraboloid x=y^2+z^2 and the plane x=16 Note: The triple integral must be performed in Cartesian coordinates. Homework EquationsThe Attempt at a Solution I calculated the answer numerically using...

Hello. Is there some easy way to convert screen coordinates (origin at the top left corner) to Cartesian coordinates?

Homework Statement Question states "The plane that contains the line r=<-2,4,3>+t<3,2-1> and is perpendicular to the plane r=<5,0,0>+s<2,1,0>+t<-1,0,1> is:" Answer is y+2z=10 Homework Equations Cross product and dot product of vectors The Attempt at a Solution I found a...

1. I found the parametric equation of a plane; \left(\begin{array}{ccc}x\\y\\z\end{ar ray}\right) = \left(\begin{array}{ccc}1\\2\\3\end{ar ray}\right) +s\left(\begin{array}{ccc}1\\1\\0\end{ar ray}\right) +t \left(\begin{array}{ccc}2\\1\\-1\end{ar ray}\right) s,t ∈ R. I was asked to...

Homework Statement Cylindrical: (5,5,53.2) Cartesian = ?? How bout Cartesian to coordinate? Any websites that shows all the conversions?

PLEASE HELP ! THANK YOU (: 1. My teacher gave us a drawing with 4 vectors on it. Vector A = 130 N and is at a 20 degree angle. Vector B = 100 N and is at a 70 degree angle. Vector C = 70 N and is on the x-axis. Vector D = 50 N and is at a 10 degree angle. Given this picture we are told to...

Homework Statement Question is "The Cartesian equation of the plane containing the line x=3t , y =1+t , z=2-t and passing through the point (-1,2,1) is?" Homework Equations \begin{array}{l} n \bullet (r - r_0 ) = 0 \\ < n_1 ,n_2 ,n_3 > \bullet < x - x_0 ,y - y_0 ,z - z_0 >...

Homework Statement Convert F into cartesian coordinates from spherical F = -4*theta*e_r + 1e_phi r(t) = 2, theta(t) = 4t, phi(t) = pi / 2 Homework Equations x = rsin(theta)cos(phi) y = rsin(theta)sin(phi) z = rcos(phi) The Attempt at a Solution Where I'm having problem is converting F into...

I have 3 circles, all cleverly plotted so as to touch the unit circle just once: x^2+y^2=1 (1) (x+1)^2+(y-1)^2=3-2\sqrt{2} (2) (x-\frac{\sqrt{7}}{2})^2+(y-\frac{1}{2})^2=3-2\sqrt{2} (3) What I need is a circle (in general form like those above) that touches all 3 circles just once...

this is just a simple question For a plane in vector form, can the cartesian equation (Ax+By+Cz+D=0) be found by finding the cross product of the two vectors? My understanding is that A, B and C are the components of the normal of the plane, which can be found by doing the cross product...

Hey everybody, \int_{B(0,\epsilon)} log \frac{1}{r} \ dxdy \ = \ \int^{2\pi}_{0} d\theta \ \int^{\epsilon}_{0} log \frac{1}{r} \ rdr when r = r(x,y) and B is a small ball with radius \epsilon Is this right? I haven't done this in forever and I need to be sure. Thanks!

Homework Statement A particle moves in a two-dimensional orbit defined by: x(t)= A(2\alphat-sin(\alphat) y(t)= A(1-cos(\alphat) a) Find the tangential acceleration a_t and normal acceleration a_n as a function of time where the tangential and normal components are taken with respect to the...

Homework Statement Convert the following cylindrical coordinate vector to a Cartesian vector: \overrightarrow{A}\,=\,\rho\,z\,sin\,\phi\,\hat{\rho}\,+\,3\,\rho\,cos\,\phi\,\hat{\phi}\,+\,\rho\,cos\,\phi\,sin\,\phi\,\hat{z} Homework Equations...

Homework Statement Transform the vector below from Cartesian to Cylindrical coordinates: Q\,=\,\frac{\sqrt{x^2\,+\,y^2}}{\sqrt{x^2\,+\,y^2\,+\,z^2}}\,\hat{x}\,-\,\frac{y\,z}{x^2\,+\,y^2\,+\,z^2}\,\hat{z} Homework Equations Use these equations...

Converting from Cartesian to Cylindrical coords - but division by zero! Homework Statement Let's say I want to convert the point P(0, -4, 3) to cylindrical. To convert from Cartesian to Cylindrical coordinates, one must use the formulas listed below. Homework Equations...

Hello, What is the best way to determine direction, force, and velocity in three dimensional Cartesian coordinates? Explanation: I am writing a program to do some star motion simulations. I will edit in some stars, give them their mass, along with initial position and velocity, and see what...

This should be relitively simple: y = x ... convert to spherical coords: p*sin(r)*sin(t) = p*sin(r)*cos(t) which reduces to... sin(t) = cos(t) tan(t) = 1 (is this right?) t =~ 0.78... (Can i get a nice fraction for this?) Any help is appreciated. - glog

Homework Statement Two forces act on an object at an angle of 50°. One force is 150 N. The resultant force is 200 N. Find the second force and the angle that it makes with the resultant.Homework Equations Ux=|U|cos(theta) Uy=|U|sin(theta) The Attempt at a Solution Basically I began by...

Change the Cartesian integral to the equivalent polar integral and evaluate: Integral of (x dx dy), limits of integration are from 0 <= y <= 6, 0 <= x <= y. --------------- I don't need help as much in evaluating the integral as just setting it up right. To change this to a polar...

should every whole number that curve x crosses be taken into consideration when constructing a polar graph? For example, when y=1 is crossed, should the radius be drawn on the polar graph if the x value is not an exact, uh, pi number (for example instead of .77 which is pi/4 the x value that...

x = 2cot t y = (sin t)^2 t is greater than 0 but less than or equal to pi/2 The cartesian can be found using trig identities to be: y = 8/ (4+ x^2) What would be the range of the cartesian equation? I think it would be x is greater than or equal to 0, since when t = pi/2, x =...

I have been trying to derive a set of equations for a new Cartesian coordinate system after a rotation of an original coordinate system. This is what I did: 1) I transformed the Cartesian coordinates (x,y,z) into spherical coordinates (r,p,q): x= r cos(q) cos(p) y= r cos(q) sin(p)...

Homework Statement The problem is :''Resolve the cartesian unit vectors into their cylindrical components(using scale factors) The Attempt at a Solution It's simple to do the inverse(resolving cylindricl unit vectors into cartesian components),but I'm having some ''trouble'' with the...

4 Questions: (1 + i) / (1 - i) Ans: i (2 + 3i) / (5 - 6i) Ans: (-8+27i)/61 1/i - (3i)/(1-i) Ans: (3-5i)/2 i^123 - 4i^9 - 4^i Ans: -9i Could someone please explain the method (detailed) as to how these answers were obatined? I understand other questions in the same...

So if we have sets A X B where A is (a_n, b_m) and C X D where C is (c_o, d_p), the cartesian product of the sets is (A X B) X (C X D) [(a_n, b_m, c_o, d_p)]. Is this correct? And thus, do parenthesis matter at all in Cartesian products? What about order? Is (a_n, b_m) equivalent to (b_m, a_n)?

Can you prove the following theory of cardinality for a Cartesian product, - \left|\:A\:\right|\:\leq\:\left|\:A\:\times\:B\:\right|\: if\: B\neq\phi In English, The cardinality of a set A is less than or equal to the cardinality of Cartesian product of A and a non empty set B.

Homework Statement This is actually a programming assignment, however it's very math involved. Given a set of points in R3 (x,y,z coordinates plus a weighted value) that are known to be coplanar, I need to draw an appropriately rotated, scaled, and colored plane intersecting the data. We...

Homework Statement Convert the point `(rho,theta,phi) = (6, (5pi)/4, pi/2)` to Cartesian coordinates. Give answers as positive values, either as expressions, or decimals to one decimal place. The Attempt at a Solution {x}=r*sintheta*cosphi {y}=r*sintheta*sinphi {z}=r*costheta So...

How do you draw an Cartesian 3D-axis-system? The Y-axis seems to have some perspective; what's the position of the observer? What's the 'way' of placement, and why? All 'links' are welcome. Dank u.

Homework Statement Replace the polar equation by an equivalent Cartesian (rectangular) equation. Then identify or describe the graph. ****Let's just make x = theta because I can't find a theta symbol***** r = 2cos(x) + 2sin(x) Homework Equations none? The Attempt at a...

Homework Statement When dealing with an integral integrated with respect to dxdy, I can convert this to polar coordinates, and then integrate with respect to dr d\theta. But I have to multiply with a "r" before integrating. If I am dealing with an integral with respect to dydz, I can...

Find a Cartesian equation for the curve. 18=rcos \theta \frac{\ 18}{cos \theta}= \sqrt{x^2+y^2} how do I get rid of the cosine?

[SOLVED] Latitude Longitude -&gt; Polar Form -&gt; Cartesian Coordinates Homework Statement I need to convert 46 Degrees North 80 Degrees west into Cartesian coordinates, based on the assumption that the Earth is a sphere (althought it's not). Homework Equations...

Homework Statement Reduce these parametric functions to a single cartesian equation: $\displaylines{ x = at^2 \cr y = 2at \cr} $ $\displaylines{ x = 3{\mathop{\rm Sec}\nolimits} \left( \alpha \right) \cr y = 5{\mathop{\rm Tan}\nolimits} \left( \alpha \right) \cr} $...

Homework Statement Intrinsic eqn of a curve is s = 12(sin \varphi)^{2} where s is length of arc from origin and \varphi is angle of tangent at a point with x axis. Show the cartesian eqn is (8-x)^{\frac{2}{3}}+y^{\frac{2}{3}}=4Homework Equations^{} \frac{dy}{dx}=tan\varphi...

Homework Statement The polar coordinates of a point are r=6.00 m and theta 250. What are the Cartesian coordinates? X=? Y=? Homework Equations Cos=adj./hyp. sin=opp./hyp The Attempt at a Solution Would I just need to calculate the cos and sin? That is, I would just do sin...

Homework Statement I solved this following problem but I am not sure whether I did this right: convert (1/(2^j)) to cartesian form. Homework Equations The Attempt at a Solution re^j\theta = a+jb a=r cos \theta= cos -\pi/2 b= sin -\pi/2 = -1 1/(2^j) = 2^-j...

I'm a bit stuck here, my question asks me to prove that the product of 2 enumerable sets is indeed enumerable with an argument or a counterexample. I pretty much have no idea on how to proceed, although i know that the product is enumerable

Wikipedia details the technique for converting from toroidal coords to cartesian. How do you convert the other way? *EDIT* Is there any free (or nearly free) software which allows you to solve algebraic equations and express variables in terms of existing formulae, AND supports sin, cos, tan...

Homework Statement Give a Cartesian equation for the parametric curve x(t)=3sin(2t) and y=4cos(2t) Homework Equations The Attempt at a Solution I'm not sure if I'm doing this right since x^2+y^2=1 I thought sin^2(2t)+cos^2(2t)=1 should be the right answer am i wrong so...

Homework Statement Use separation of variables in cartesian coordinates to solve the infinite cubical well (or "particle in a box"): V(x,y,z) = \{^{0, if x, y, z are all between 0 and a;}_{\infty , otherwise.} Homework Equations Well, I've been trying to use \frac{1}{2}mv^{2} + V =...

hi, all, run into one geometry problem: I have two 3-D Cartesian systems, A and B. they share the same original. the coordinate (2,3,3) in B system is the same vector as (118,2090,1000)in A system( there may be scale difference, but they are the same direction); then what is the vector in B...