What is Xy-plane: Definition and 21 Discussions

A Cartesian coordinate system (UK: , US: ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length. Each reference line is called a coordinate axis or just axis (plural axes) of the system, and the point where they meet is its origin, at ordered pair (0, 0). The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin.
One can use the same principle to specify the position of any point in three-dimensional space by three Cartesian coordinates, its signed distances to three mutually perpendicular planes (or, equivalently, by its perpendicular projection onto three mutually perpendicular lines). In general, n Cartesian coordinates (an element of real n-space) specify the point in an n-dimensional Euclidean space for any dimension n. These coordinates are equal, up to sign, to distances from the point to n mutually perpendicular hyperplanes.

The invention of Cartesian coordinates in the 17th century by René Descartes (Latinized name: Cartesius) revolutionized mathematics by providing the first systematic link between Euclidean geometry and algebra. Using the Cartesian coordinate system, geometric shapes (such as curves) can be described by Cartesian equations: algebraic equations involving the coordinates of the points lying on the shape. For example, a circle of radius 2, centered at the origin of the plane, may be described as the set of all points whose coordinates x and y satisfy the equation x2 + y2 = 4.
Cartesian coordinates are the foundation of analytic geometry, and provide enlightening geometric interpretations for many other branches of mathematics, such as linear algebra, complex analysis, differential geometry, multivariate calculus, group theory and more. A familiar example is the concept of the graph of a function. Cartesian coordinates are also essential tools for most applied disciplines that deal with geometry, including astronomy, physics, engineering and many more. They are the most common coordinate system used in computer graphics, computer-aided geometric design and other geometry-related data processing.

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  1. neroE

    Electric Field due to a disk of radius R in the xy-plane

    Hello, This question, which I found in various electricitiy and magnetism books (e.g. Introduction to electrodynamics grif.). There are many variations of this question, I am mainly interested in the following setup of it: -Suppose there is a charged disk of radius R lying in the xy-plane, and...
  2. lambdajitsu

    A Lagrangian for straight line in XY-plane (dependent on time)

  3. WMDhamnekar

    MHB How is z=2xy a Hyperbolic Paraboloid in the rotated 45° in the xy-plane?

    How to prove that every quadric surface can be translated and/or rotated so that its equation matches one of the six types of quadric surfaces namely 1) Ellipsoid 2)Hyperboloid of one sheet 3) Hyperboloid of two sheet 4)Elliptic Paraboloid 5) Elliptic Cone 6) Hyperbolic Paraboloid The...
  4. W

    A condition for an object to return to the xy-plane

    Homework Statement [/B] An object of m-mass is to be thrown from xy-plane with an initial velocity ##\mathbf v_0 = v_0\mathbf e_z \, (v_0 > 0)## to a force field ##\mathbf F = -F_0 e^{-z/h}\mathbf e_z\,## , where ##F_0, h > 0## are constants. By what condition does the object return to...
  5. K

    Calculating Line Integral in xy-Plane

    Homework Statement Calculate the line integral ° v ⋅ dr along the curve y = x3 in the xy-plane when -1 ≤ x ≤ 2 and v = xy i + x2 j. Note: Sorry the integral sign doesn't seem to work it just makes a weird dot, looks like a degree sign, ∫.2. The attempt at a solution I have to write something...
  6. Vital

    Graph r = 6 cos() issues with plotting on xy-plane

    Homework Statement Hello! Last week I have came here for the help related to this problem. I am creating a new thread to describe the issue more precisely. I will be grateful for your help and explanation. I post the explanation for the book first accompanied by attached pictures, and below I...
  7. SquidgyGuff

    Laplace's Equation and the potential above the xy-plane

    Homework Statement Essentially it gives the potential above the xy-plane as and I am tasked with verifying it satisfies laplace's equation, determining the electric field, and describing the charge distribution on the plane. Homework Equations then The Attempt at a Solution As far as I...
  8. W

    Using force vector to integrate work in xy-plane

    Hello, I picked up a challenging problem (at least to me) and I'm having difficulties. 1. Homework Statement An object moves in xy-plane from point O = (0; 0) to point A = (1 m; 0) and from there to point B = (1 m; 2 m). All this time when the object moves a force \vec F = ax2\vec i + by\vec...
  9. W

    Calculus III: Find a line perdendicular to XY-plane?

    Homework Statement [/b] "Find an equation for the line through the point P = (1, 0, −3) and perpendicular to the xy-plane," obviously this includes vector <0, 0, 1> I am in Calc III and need help understanding how to do this TYPE of problem. Please include step-by-step instructions and...
  10. B

    Intersection of a sphere and a cone. (projection onto the xy-plane)

    Part of a chapter review problem. Say you have a sphere centered at the origin and of radius 'a'. And you have a (ice-cream) cone which has it's point at the origin and phi equal to ∏/3. How do I find the equation of their intersection? Which is the projection onto the xy plane...
  11. J

    Circular ring in xy-plane with current, find current density

    Homework Statement Consider a circular ring of wire of radius a that resides in the x-y plane through the origin. The center of the ring coincides with the origin and you can regard the thickness of the wire to be infinitesimal. a. Given that a current I flows in the ring, find an...
  12. N

    Find Surface Area of Sphere Part Above xy-Plane & Within Cylinder

    Find the surface area of that portion of the sphere x^2 + y^2 + z^2 = a^2 that is above xy-plane and within the cylinder x^2 + y^2 = b^2 , 0 < b < a Solution.. i try to find fx and fy.. http://imageshack.us/f/594/33049204.jpg/" how am i going to proceed?
  13. S

    Vector Valued Function and values of t parallel to the xy-plane

    Homework Statement So, the problem is this: Find all values of t such that r'(t) is parallel to the xy-plane. And my equation is: r(t)=(Squareroot(t+1) , cos(t), t4-8t2) Homework Equations Well, I will definitely have to know how to take the dirivative of the given vector valued...
  14. K

    Conservative force on XY-Plane

    Homework Statement [PLAIN]http://img293.imageshack.us/img293/9080/omgay.jpg Homework Equations ? The Attempt at a Solution ?? I'm already lost at where to begin.
  15. K

    Understanding Line in R^3 Parallel to XY-Plane: Help Needed

    What does it mean if a line in R^3 is parallel to the xy-plane but not to any of the axes. I really don't know what this means in terms of how the parametric and symmetric equations of the line should look. Please help. Thanks.
  16. S

    Volume of region R between paraboloid and xy-plane

    Homework Statement So my question is: what is the volume of the region R between the paraboloid 4-x^2-y^2 and the xy-plane? Homework Equations I know how to solve it, it is a triple integral, but how do you find the limits of integration? The Attempt at a Solution Do I set x=0...
  17. K

    Diff. paths of a Force in xy-plane

    [SOLVED] diff. paths of a Force in xy-plane Homework Statement A force acting on a particle in the xy-plane is given by \vec{F} = (2yi + x^2j) where x and y are in meters. The particle moves from the origin to a final position having coordinates x = 5.00m and y = 5.00m...
  18. P

    Find Length of r(t) on [0,3]: Sketching the Plane Curve in xy-Plane

    Sketch the plane curve in the xy-plane and find its length over the given interval: r(t) = (6t-3)i + (8t+1)j on [0,3] Here's what I've got so far: r'(t) = 6i + 8j llr'(t)ll = sqrt of 6^2+8^2 = 10 s = integral 0-3 10dt = 10x ]0 to 3 = [30-0] = 30I just need help on how to sketch this plane...
  19. E

    Three Charged Particles in an xy-plane

    Question: A particle of charge 4.96 nC is placed at the origin of an xy-coordinate system, and a second particle of charge -1.95 nC is placed on the positive x-axis at x = 3.99 cm. A third particle, of charge 6.04 nC is now placed at the point x = 3.99 cm, y = 3.05 cm. Part A Find the...
  20. Reshma

    Particle of Mass M Moving in XY-Plane: Potential Energy & Orbit Analysis

    A particle of mass M is free to move in the horizontal plane(xy-planne here). It is subjected to force \vec F = -k\left(x\hat i + y\hat j\right), where 'k' is a positive constant. There are two questions that have been asked here: 1] Find the potential energy of the particle. \vec \nabla...
  21. W

    Solid that lies above the square (in the xy-plane)

    Consider the solid that lies above the square (in the xy-plane) R= [0,1] X [01] and below the elliptic paraboloid z= 64 -x^2 +4xy -4y^2 Estimate the volume by dividing R into 9 equal squares and choosing the sample points to lie in the midpoints of each square. i'm not sure how you...