Cartesian Definition and 561 Threads

Homework Statement Find a bijective map g : X^{m} \times X^{n} \rightarrow X^{m + n} Homework Equations The Attempt at a Solution I don't even know where to begin. How would I map X^{m} \times X^{n} in the first place? How could I map X^{m + n}?

Is the cartesian product (A \times B) the set of ALL POSSIBLE ordered pairs (a, b) such that a is an element of A and b is an element of b, or is it simply the set of "all ordered pairs?"

Homework Statement Find a Cartesian equation for the curve and identify it. r = 3sin(θ)Homework Equations The Attempt at a Solution I know that the answer is as follows... r^2=3(r*sin(\theta)) x^2+y^2 = 3y x^2 + (y-\frac{3}{2})^2 = (\frac{3}{2})^2 I understand everything but the last part...

Homework Statement 6...y ∫...∫ x dx dy 0 ...0 The Attempt at a Solution for reference: π=pi 6...y ∫...∫ x dx dy 0 ...0 y=6=x=6. rcosΘ=6 r=6/cosΘ goes to π/2 6secΘ ∫ ...∫... r cosΘ r dr dΘ π/4...0 π/2.....r=6secΘ ∫ ... [((r^3)/3)cosΘ] dΘ π/4......r=0 π/2...

Homework Statement Velocity vector, v: v = (yi + xj) / (x^2 + y^2 + z^2)^(3/2) "Re write "v" in spherical polar coordinates and unit vectors" Homework Equations Obviously r = (x^2 + y^2 + z^2)^(1/2) theta = tan^(-1)((x^2 + y^2)^(1/2)/z) phi = tan(^-1)(y/x) The Attempt at a Solution...

I'm trying to create a program which will do these calculations. I am given Latitudes, Longitudes, and ellipsoidal heights for ellipsoids and another set of x, y, and z coordinates. I am so confused looking at how to convert these things. I know I need to iterate in order to go from cartesian to...

Howdy everyone, I'm on a quest for something that is proving a bit elusive at the moment: a Cartesian to polar transform (along with its inverse) for \mathbb{R}^4. I'm well aware of how to derive the transform for both \mathbb{R}^2 and \mathbb{R}^3, as it is just a matter of looking at the...

Hello I am carrying out some analysis on the magnetic field generated over a 3D region by a single current loop. The present form of the equations is in cylindrical coordinates and is as follows \vec{B}={Brc,0,Bz} There is no angular component in this present from. Note: The following website...

Homework Statement Okay here's the problem: Consider the region R interior to a circle(of r =2) and exterior to a circle(r=1). 1.Using cartesian coords and double integral, calc the area of annulus. 2. repeat calculation above but using double integral with polar coords The...

We learned about cartesian coordinates briefly in class and i didnt completely understand them. I am not looking for an answer but rather the process on how to get to an answer in cartesian coordinates, for instance, in this example: A point on a polar coordinate system is located at r=2.0...

Homework Statement Show that E_z = \frac{p}{4 \pi \epsilon_0} \left( \frac{3z^2}{r^5} - \frac{1}{r^3} \right) is equivalent to the electric field on the positive z-axis from E_r = \frac{2 p \cos \theta}{4 \pi \epsilon_0 r^3} Homework Equations The unit normal for a sphere, sin0cos%...

Homework Statement Write down the general cartesian equation of a vertical plane (parallel to the z-axis), a non-vertical plane and a horizontal plane (parallel to the x; y-plane) together with their normal vectors. Find the cartesian equations of the line of intersection of the plane 5x + y ¡...

Homework Statement This seems like a trivial question (because it is), and I'm just not sure if I'm doing it right. I have vector in cartesian coordinate system: \vec{a}=2y\vec{i}-z\vec{j}+3x\vec{k} And I need to represent it in cylindrical and spherical coord. system Homework...

Homework Statement Convert the following Cartesian equation to polar form. x^2/9 + y^2/4 = 1 Homework Equations r*cos(t)=x r*sin(t)=y r=Sqrt(x^2 + y^2) y/x = Arctan(t) The Attempt at a Solution I get ugly looking things like r^2(cos^2(t)/9 + sin^2(t)/4) = 1 but being a simple ellipse (edit...

I just did a quiz in a lecture and walked out crying. There was one question (which probably seems very easy to most :/ ) were you had to convert polar equations to cartesian ones. We also had to draw the cartesian graphs (2D). a) rcos(th) b)r=2asin(th) c)r^2sin2(th)=2k...

The problem states: Let R and S be nonzero rings. Show that R x S contains zero divisors. I had to look up what a nonzero ring was. This means the ring contains at least one nonzero element. R x S is the Cartesian Product so if we have two rings R and S If r1 r2 belong to R and s1 s1...

Homework Statement If D=3i–2j and E=–7i+5j … (a) What is |D|? (b) What is |E|? (c) What are the vectors D+E and E–D? !THERE ARE SUPPOSED TO BE HATS OVER THE VARIABLES! I would put up an attempt at the problem if I even knew how to attempt it.

Homework Statement Give the Cartesian equation of the following hyperplane: The plane spanned by (1,1,1) and (2,1,0) and passing through (1,1,2)Homework Equations The Attempt at a Solution I keep getting 4 = -2x(sub1) + -2x(sub2) +x(sub3). However, the answer is x(sub1) - 2x(sub2) + x(sub3) =...

Homework Statement Give a Cartesian equation of the given hyperplane The plane passing through (1,2,2) and orthogonal to the line x = (5,1,-1) + t(-1,1,-1)Homework Equations The Attempt at a Solution So I've looked at this for a few hours and still can't figure out how to do it. It's supposed...

Homework Statement 17. Let U = f(x; y; 0) : x 2 R; y 2 Rg, E1 = f(x; 0; 0) : x 2 Rg, and E3 = f(0; 0; x) : x 2 Rg: Are the following assertions true or false? Explain. (a) U + E1 is a subspace of R3: (b) U  E1 is a direct sum decomposition of U + E1: (c) U  E3 is a direct sum...

I'm having issues getting converting Polar functions to Cartesian functions. Take for example: rcos(\theta)=1 I just figured that since it was going to always equal the same thing, and because x=rcos(\theta) that the Cartesian equation was x=1, and I was right. However logic fails...

Homework Statement The vector V is given by V = (5.0x-12.0y )m. What is W such that V + W = -5|V|x? Homework Equations |v| = (vx2 + vy2)1/2 The Attempt at a Solution I was unsure of what I did to subtract vector v- I know the negative vector has the same magnitude but opposite...

Homework Statement Hi there. Well, I have the next exercise, which I've solved, but I don't know if the solution I got is the right one. It says Given the next region on spheric coordinates find the expression for it in rectangular coordinates, and plot...

Homework Statement Write the vectors B,D, and F in the figure in Cartesian form, with unit vectors. (See attachments) Homework Equations ax = a cos theta ay = a sin theta where a = magnitude of vector a, and theta = the angle vector a makes with the positive direction of the x axis...

My main issue is trying to understand the question being asked (is it asking for the magnitude of the resultant vector for speed?) Homework Statement Particle 1 is moving on the x-axis with an acceleration of 5.00 m/s^2 in the positive x- direction. Particle 2 is moving on the y- axis with...

Express the following in cartesian curves in polar form i) 4x-5y=2 Not sure how to do this ii) (x-3)^2+(y-4)^2=25 r=9cos16(theta) Is this correct ? Any help would be great

Homework Statement Hi there. Hi have in cylindrical coordinates that \theta=\displaystyle\frac{\pi}{3}, and I must make the graph, and take it into cartesian coordinates. How should I do? I've tried this way: \begin{Bmatrix}x=r\cos\displaystyle\frac{\pi}{3}\\y=r\sin\displaystyle\frac{\pi}{3}...

Homework Statement In the attachments, you will see the problem and my answer. Is my answer correct?

Homework Statement A relation p is defined on R^2 (fancy R, as in Reals) by (a,b)p (c,d) if a+d=b+c Show that p is an equivalence relation. b) Consider R^2 to be the Cartesian Plane. Describe p's equivalence classes geometrically. (Consider which points will be in the particular...

Has to convert B6-1 into B6-2 Source Transport Phenomenon 2nd ed -

This is going to be a weird question, but in textbooks when we're given the two spaces R^n and R^m, and they say something about R^(n+m), then are they referring to ordered pairs of ordered pairs? That is, if x is in R^n and y is in R^m, then R^(n+m) is the set of all ordered pairs (x,y). So for...

The two sets of matrices: {G_1} = i\hbar \left( {\begin{array}{*{20}{c}} 0 & 0 & 0 \\ 0 & 0 & { - 1} \\ 0 & 1 & 0 \\ \end{array}} \right){\rm{ }}{G_2} = i\hbar \left( {\begin{array}{*{20}{c}} 0 & 0 & 1 \\ 0 & 0 & 0 \\ { - 1} & 0 & 0 \\ \end{array}} \right){\rm{...

Homework Statement determine the cartesian equation of the plane that contains the following lines: L1: r= (4,4,5) + t(5,-4,6) L2: r= (4,4,5) + s(2,-3,-4) Homework Equations I kno I'm supposed to use the equation Ax + By + Cz + D. but i don't know how to use it with this type of...

Dear all, How can I derive the volume of a spherical cap by integration and using the Cartesian coordinate system. The sphere is located at the (0,0,0) coordinates and its radius is set to r. The height of the cap is also set to (r-h). I googled a lot but I couldn't find it. I would...

I'm posting here, in the math forum, because my question is about handling the math of the problem. On my website there are a number of simulations (in the form of Java applets), and among them is a http://www.cleonis.nl/physics/ejs/ballistics_simulation.php" . The ballistics simulation is...

Homework Statement Write the Cartesian equation for the plane containing the point (2,-1,8) and perpendicular to the line [x,y,z] = [1,-2,-3] + s[5,-4,7]. The Attempt at a Solution The situation is that I have my Calc. + Vectors exam tomorrow morning and I'm just going through some...

Homework Statement See attachment. Change the Cartesian integral into an equivalent polar integral, then evaluate the integral. I have no problems at all converting the actual function I am integrating or the integration itself, it is just the limits I cannot do. I've posted two...

Hi, I follow the instruction in wikipedia to make a Cartesian diver (Coca Cola bottle + eyedropper), and it works well. I press the bottle, the eyedropper sinks; I release, it floats. However, if I turn the bottle upside down, the eyedropper sinks and it never floats again. That means the...

Homework Statement 1. Establish the vector identity \nabla . (B x A) = (\nabla x A).B - A.(\nabla x B) 2. Calculate the partial derivative with respect to x_{k} of the quadratic form A_{rs}x_{r}x_{s} with the A_{rs} all constant, i.e. calculate A_{rs}x_{r}x_{s,k} Homework Equations The...

Hi all, I have been trying to write code to convert from cartesian to fractional coordinates. I think everything is correct in my code (i have used wikipedia as reference - http://en.wikipedia.org/wiki/Fractional_coordinates), but still, the code doesn't work for some test values. The code is...

Homework Statement Hi I am converting from Cartesian co-ordinates to cylindrical co-ordinates systems and can do the conversion fine, but am unsure about how to convert the limits. Q) Region V is given in Cartesian by: F(x,y,z) = xi+yj+z(x^{2}+y^{2})k Where x^{2}+y^{2} \leq 1...

Homework Statement Prove that \forall sets A, B, C , if B\subseteq C, then A \times B \subseteq A \times CHomework Equations The Attempt at a Solution Haven't done set theory proofs in a while. Does this suffice in proving the statement?: Let x \in B be arbitrary. Assuming B \subseteq C...

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, using only cartesian vectors. Homework Equations The Attempt at a Solution Over here, I am very confused...

Homework Statement Use Cartesian vectors in two-space to prove that the line segments joining midpoints of the consecutive sides of a quadrilateral form a parallelogram. Homework Equations We could say vectors a and b a = [a1, a2] b = [b1, b2] The Attempt at a Solution Am...

Homework Statement A flow field is considered to be steady two-dimensional and can be described by the following velocity components in the xy- or r\theta-plane at the front half of the cylinder: u_r=V\cos\theta\left(1-\frac{a^2}{r^2}\right)...

Homework Statement Find the vector equation of the line that passes through the point Q(2,0,-5) and is perpendicular to both the vectors m=(0,1,4) and n=(-2,-1,3). Homework Equations vector equation of a line: (x, y, z)=(x0,y0,z0) + t(a,b,c) cartesian equation of a line...

Homework Statement Is there a univeral conversion formulae to convert Azimuth and Elevation to Lat Lon or Cartesian X,Y,Z? Homework Equations So far, I have only been able to source out and successfully convert Cartesian X,Y,Z to Lat Long Alt. The Attempt at a Solution No findings...

We understand that Lat Long Alt can be derived from 3D Cartesian (X,Y,Z) but does a 5D Cartesian (X, Y, Z, Vx, Vy) does the extra mile to provide a more precise conversion to Lat Long Alt with the additional velocity data?

Just wanted to confirm. Cartesian scalar equation of plane refers to equation of plane right? As in Ax+By+Cz=D. which i think is the vector equation of a plane. I'm getting confused and need clarification thank you edit= ok sorry.. i think i got it figured out =p scalar is there because...

Hi I pretty much can't get past the first chapter in my physics book until I master the vector representation of polar coordinates. Every explanation I've read thus far has confused me, I keep thinking in Cartesian terms so I think it'd be great to convert a vector equation from cartesian to...