What is Cross: Definition and 1000 Discussions

A cross is a geometrical figure consisting of two intersecting lines or bars, usually perpendicular to each other. The lines usually run vertically and horizontally.
A cross of oblique lines, in the shape of the Latin letter X, is also termed a saltire in heraldic terminology.
Throughout centuries the cross in its various shapes and forms was a symbol of various beliefs. In pre-Christian times it was a pagan religious symbol throughout Europe and western Asia. In ancient times, the effigy of a man hanging on a cross was set up in the fields to protect the crops. The cross was even considered a male symbol of the phallic Tree of Life; thus it often appeared in conjunction with the female-genital circle or oval, to signify the sacred marriage, as in Egyptian amulet Nefer with male cross and female orb, considered as an amulet of blessedness, a charm of sexual harmony.

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  1. W

    Cross products- how to determine the angle?

    Consider the following problem: You strike a pool ball (radius R) at some height h above the table, so that it immediately rolls without slipping. At what height h should you strike it? I worked out the problem and got 1.4R, which is indeed the answer. However, at one point I made the...
  2. R

    How to Calculate Cross Section for Scalar-Neutrino Interaction?

    Homework Statement Hi. I'm trying to calculate the cross section for this process: where \phi is a massive neutral scalar, N is a massive Majorana neutrino and \nuL is the normal SM neutrino. Homework Equations N/A The Attempt at a Solution Apparently the answer should be something like...
  3. D

    Calculating Cross Section from Neutron Absorption in a Gold Foil

    Homework Statement In an experiment carried out with a beam of thermal neutrons it is found that on traversing a 2mm thick foil of 197Au, some 70% of the neutrons are removed. What is the total thermal neutron cross-section for this isotope of gold? (Density of gold: 19300 kg m-3) Homework...
  4. D

    Queries on Signal Processing - Cross Correlation

    I'm new to the field of signal processing and currently reading a paper which it uses cross-correlation of two signals for detecting some machine failures. But I'm confused with the complex conjugate in the equations. Take equation from wikipedia as example: (f\star g)(t)\equiv \int_{-\infty...
  5. Q

    PDE Iteration with cross product

    This may be more of a MATLAB question, and if so, I do apologize for posting this in the wrong place. I am doing a project on the Buttke scheme, which is a numerical approximation to the Biot-Savart Law. I am almost finished, but I am having trouble writing the code. The scheme is...
  6. C

    How should I use slow cross fast rule?

    Homework Statement http://i.imgur.com/a36Mj.png Homework Equations The Attempt at a Solution Slow cross fast gives me positive z direction...
  7. H

    Solving for R2: Calculating Vector Cross Product

    I am trying to figure out the following If R2 = 1.043j -1.143k Then how can R2 = 1.547
  8. M

    Finding volume using cross sections

    Homework Statement find the volume of the solid whose base is the region bounded by y^2=9x and x=1 in the xy-plane. each cross section perpendicular to the x-axis is an isosceles right triangle with its hypotenuse in the xy-plane. Homework Equations V=\int_{a}^{b}A(x)dx The Attempt...
  9. E

    Proving Cross Product Equation: A x (B + C) = A x B + A x C

    Problem: Prove A x (B + C) = A x C + A x B Related equations: Cross product Attempts: Not even remotely sure where to start with this, other than I need to use the cross product rule.
  10. D

    Inverse Muon Decay differential cross section

    Why is it that the differential cross section for processes like Inverse Muon Decay (IMD) are always given in the CM frame? Every paper I have seen that discusses Inverse Muon Decay gives the differential cross section in CM frame. Is it very hard to calculate the differential cross section in...
  11. P

    Proving PoSet of cross product

    Homework Statement (Z, Q) and (W, S) are two partially ordered sets. There is a relation I on Z x W (Z cross W) that is defined... for all (a, b), (c, d) in Z x W, set (a, b) I (c, d) if and only if aQc and bSd. How does one prove that (Z x W, I) is a partially ordered set? Homework...
  12. D

    Cross product for complex vectors

    I was wondering, is the definition of the cross product the same for complex vectors? And if it is, then how is its geometric interpretation, that is ||\mathbf{a}\times\mathbf{b}||=||\mathbf{a}|| \; ||\mathbf{b}|| \sin\theta Thanks.
  13. M

    Spatial Cross Correlation help ly needed

    Spatial Cross Correlation help urgently needed! I am working on Cross Correlation at the moment with varying degrees of success. I have figured out how to do Cross and Auto Correlation but am lost tryng to understand spatial CC. I can't seem to find any helpful resources for what I am working...
  14. G

    Pipework Networks (Hardy cross method)

    Hi everyone, I have a 2nd year fluid mechanics question! Homework Statement I'm having trouble gripping what this question is looking for: Explain and Discuss the rationale implications of assuming that the head loss in each section of the pipe network is proportional to the square of the...
  15. P

    Calculate cross correlation manually

    I want to know how one might calculate the cross correlation of two signals by hand. I know that there are a myriad of software applications that will do this for me but I want to understand how it is done by hand. I'm using the expression: ccxy[k] = ∑ x[n]. y[n+k] I'm just not too sure what the...
  16. J

    Deriving cross product and dot product, stuck at beginning.

    Homework Statement Assuming that ∅ is a differentiable scalar valued function and F a differentiable vector field, derive the following identities. a)∇(dotted with)(∅F) = ∇∅(dotted with)F + ∅∇(dotted with)F b)∇(crossed with)(∅F) = ∇∅(crossed with)F + ∅∇(crossed with)F Homework Equations The...
  17. N

    What is the neutron scattering differential cross section?

    What is the neutron scattering Differential Cross section .. simple definition? ... Thanks
  18. S

    Why is my Cross Product Calculation Resulting in a Negative Value?

    Hi all, Just having some trouble understanding a certain example of cross product. It's actually for physics, but figured it belongs in this forum. In the question I am supposed to cross (dl)y hat with (x1)x hat. So I go (0 dl 0) x (x1 0 0) = (-x1dl)z hat. But turns out the answer the...
  19. D

    Can the Cross Product be Generalized Using the Dot Product?

    I know the cross product and dot product of euclidean space R^3. But I wanted to know if there is a way of thinking the cross product "in terms of" the dot product. That is because the dot product can be generalized to an inner product, and from R^3 to an arbitrary inner vector space (and...
  20. M

    Finding the Cross Product for Angular Momentum

    Homework Statement For the general case. I need help finding the cross product for the angular momentum. Say you have a particle at a position r= xi+yj+zk with a velocity of xi+yj+zk and a known mass. How do you find the angular momentum? Homework Equations L=mvr The Attempt at a...
  21. G

    Finding when two runners cross

    Homework Statement Homework Statement Runner A is initially 6.0 km west of a flagpole and is running with a constant velocity of 4.8 km/h due east. Runner B is initially 6.6 km east of the flagpole and is running with a constant velocity of 8.6 km/h due west. What will be the distance of the...
  22. D

    I must be discomprehending the Rutherford scattering cross section.

    I do not understand the interpretation of the http://hyperphysics.phy-astr.gsu.edu/hbase/rutsca.html" . To me, that equation says: (1) for a given θ, the proportion of particles exiting at θ does NOT depend on mass or charge; (2) if you integrated over all possible scattering angles, you...
  23. S

    Vector. Is there an inverse of dot and cross product?

    Given the following cross product equation: \vec{A}\times\vec{B}=\vec{C} How to express \vec{A} in term of \vec{B} and \vec{C} (or \vec{B} in term of \vec{A} and \vec{C} ). I think the question I want to ask can also be rephrased as if one was told that a known vector when cross product with...
  24. A

    Using cross product to determine if vectors are parallel

    My question is simple: I understand that if u x v = 0 , then u and v are parallel, but what does that 0 mean? You can't obtain 0 by crossing two vectors. By 0, does it mean (0,0,0)?
  25. C

    Evaluating stiffness with varying MOE through cross section

    I am replacing an exisitng solid rod with a new rod with a rod made from a different material and a different cross section. The new material has a MOE that varies with skin depth which is making it hard for me to develop an expression for stiffness (EI). The new rod has a hollow...
  26. J

    Cross products vs. dot products

    I have a question regarding cross products and dot products. What is the difference, and are there any similarities? What ARE cross products and what are their functions? What ARE dot products and what are their functions? What do we use them for? Thank you, Joyci116
  27. K

    What is the Moment Produced by a Force at the Origin?

    F = 5i + 3j Newtons acts 3 m to the right of the origin (x is horizontal and y is vertical). What moment does this force produce about the origin? Use the vector cross product. "Great works are performed
  28. S

    Derivation of the photoionization cross section

    Hallo Physics Forum, this is my first post, so please be gentle to me :). I am currently studying the relativistic photoionization process, and especially its differential cross section. Let us assume that we have a highly energetic, unpolarized photon beam traveling on the z-axis and...
  29. N

    Rhodium Thermal absorption cross section.

    Rhodium has been measured and the following values have been obtained for the resonance parameters of a well-isolated resonance Eo=1.26 ev , σo=5000 b , Γ = 0.156 ev , σs=5.5 b , Is there anyone can help me HOW to calculate the thermal absorption cross section ? I'm disparate I don't know how to...
  30. D

    Tangent plane to a surface, no need for cross product?

    For tangent plane equation z-z0 = f{x}(x0,y0)(x-x0) + f{y}(x0,y0)(y-y0) how come there is no cross product of the partial derivatives f{x} X f{y} to give the normal vector for the plane?
  31. 1

    Volume of a solid w/known cross section

    Homework Statement The base region of a solid is bounded by y=x, y=(x-1)^2, and x = 1. The cross sections are semicircles perpendicular to the x-axis. Write a riemann sum and definite integral. Homework Equations The Attempt at a Solution First, I wrote down the formula...
  32. L

    Electric potential across a cross sectional cylinder

    Homework Statement A cross-section of a cylindrical high voltage terminal (inner cylinder) of a van de Graaff generator, surrounded by an 'intershield' (middle cylinder) and a pressure vessel (outer cylinder). The gas in the pressure vessel breaks down in electric fields greater than...
  33. P

    Is there a simpler method for proving the cross product vector theorem?

    Not sure if this is the correct section. I apologize if it's not. Homework Statement For any vectors \vec{a}, \vec{b}, \vec{c} show that: (\vec{a} \times \vec{b} ) \times \vec{c} lies in the plane of \vec{a} and \vec{b} Homework Equations The Attempt at a Solution I assigned \vec{a} =...
  34. W

    Cross section - scattering of light by light

    Homework Statement Red and green laser (wavelength of 650 nm and 532 nm respectively) are directed towards each other at 20 degrees. Each laser has 5 mW power, with diameter of 1mm. Assuming the intensity of the beams are decreased by 10% each after the 'collision', estimate the upper...
  35. B

    Why does Photoionization cross section reduce with frequency?

    I'm currently starting a large comp-astro project, and trying to understand a bit of the background about heading of Hydrogen and Helium IGM clouds I am a bit confused about the the actual heating process. From the standard photoelectric effect, frequency has to pass a certain frequency (or...
  36. J

    Finding Vectors for Cross Product Problem - Explanation and Solution

    Homework Statement i) Find all vectors v such that <1,2,1> X v = <3,1,-5> ii) Explain why there is no vector v such that <1,2,1> X v = <3,1,5> Homework Equations a X b = <a_{2}b_{3} - a_{3}b_{2}, a_{3}b_{1} - a_{1}b_{3}, a_{1}b_{2} - a_{2}b_{1}) The Attempt at a Solution i) <1,2,1> X v =...
  37. A

    Perpendicular Plane to Two Given Planes

    Homework Statement Find a plane perpendicular to the two planes, X+Y=3 and X+2y-z=4 I know i take the cross product of both so i get <1,1,0> and <1,2,-1> But when i do the cross product i get x-y+z book tells me x-y-z what am i doing wrong? Not sure why the z is negative. The...
  38. QuarkCharmer

    Determinates to Calculate Cross Product

    Homework Statement Not really a homework problem, just a general question. Homework Equations Sorry, I don't yet know how to create arrays/matrices in latex (this is a gif) The Attempt at a Solution In the above image, why is c_{1} positive, c_{2} negative, and c_{3} positive? Aside from...
  39. M

    Current vs Number of wires (finding cross section of a wire)

    Homework Statement Using conductivity constant (q=1.45*10^6mA) deduce the cross-Sectional area of the wire from the slope of the Data found in the graph. Voltage was kept constant 1.00 volts The wires are each 1m long After graphing the data the Current(mA) # of parralel lines 121.4...
  40. DryRun

    Use cross product formula in R^4 to obtain orthogonal vector

    Use cross product formula in R^4 to obtain a vector that is orthogonal to rows of A Please help with first part and check if i answered the questions correctly. The matrix A = 1 4 -1 2 0 1 0 -1 2 9 -2 2 1. Use cross product formula in R^4 to obtain a vector that is...
  41. S

    Use the cross product to find the sin of an angle then prove it

    Homework Statement Leta theta be the angle between the vectors u=2i +3j -6k and v=2i + 3j+6k A) use the dot product to find cos theta b) use the cross product to find sin theta c) confirm that sin^2(theta) + cos^2(theta)=1The Attempt at a Solution I got a to be 117 degrees, but however b and c...
  42. E

    Volume of solid with given base and cross sections

    Homework Statement The base is the semicircle y = \sqrt{9-x2}(Square root of 9-x2.. i don't know why the formatting isn't showing up) where -3 <= x <= 3. The cross section perpendicular to the x-axis are squares. Homework Equations -3\int3 = A(y)dy A(y) = area of cross section...
  43. R

    Bending of a varrying cross section

    Recently, I had lab. In the lab we took different objects and measured their strain. One object had a varying cross section. The data for strain was recorded. Right now, I'm trying to make a stress strain graph, but the problem is my equation for stress. I don't know how i can take my moment of...
  44. T

    Drawing a Collection Of vectors Satisfying Cross Products

    Homework Statement Given a = <1,2,3> and b = <1,-1,-1>, sketch the collection of all position vectors c satisfying a x b = a x c Homework Equations The Attempt at a Solution I've calculated a x b = <1,4,-3> and Defining c = <x,y,z> I found a x c = <2z-3y, z-3x, y-2x>. I want to...
  45. R

    Gradient (dot) cross product of 2 differentiable vector functions

    [b]1. For two differentiable vector functions E and H, prove that (Delta (dot) (e X h) = H (dot) (delta X e) - e (dot) (Delta X h) [b]2. Cross product and dot product. The Attempt at a Solution First I took did the left side of the equation, I took the cross product of vectors e and...
  46. Dembadon

    Multi-Variable Calculus: Cross Product Expressions

    I would like to check my answers... Homework Statement Given nonzero vectors u, v, and w, use dot product and cross product notation to describe the following. A vector orthogonal to u X v and u X w A vector orthogonal to u + v and u - v A vector of length |u| in the direction of v...
  47. wukunlin

    Photon-Photon Scattering: Cross Section Calculations

    from what I know: cross section in particles physics can be seen as throwing random darts on ballons on a wall, ie the wall is stationary. but if I want to work out the cross section of two laser beams at certain angles, the analogy above wouldn't hold would it? Since photons can never to...
  48. G

    Vector question (using the cross product I think)

    Homework Statement Describe all unit vectors orthogonal to both of the given vectors: \vec{a} = 2\vec{i} - 4\vec{j} + 3\vec{k} \vec{b} = -4\vec{i} + 8\vec{j} - 6\vec{k}Homework Equations The cross product of two vectors using the determinant, then dividing by the magnitude of the vector...
  49. M

    Cross product of difference and sum of two vectors

    Homework Statement show that: ( a - b ) x (a + b ) = 2a x b and wat is its geometric interpretation ?? I'm not sure what's wrong, but i somehow got the value as 2a and not wat was required... PLease help. Homework Equations Since this is a proof, the answer I've arrived at is...
  50. N

    Physical significance of dot and cross products in electrodynamics

    i know that del.v=divergence of vector v and del x v=curl of vector v can anyone justify for the same? how dot product is physically connected to divergence property?
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