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. A

    Calculating Nuclear Cross Section for Materials

    Homework Statement What is the cross section if the density of atoms in a material is 10^26 metres-3, and 0.04% of a beam of neutrons is stopped in a 2 cm slab of the material ? Homework Equations Sigma = event rate per nuclei / incident flux The Attempt at a Solution I have...
  2. T

    Calculating exposure / dose from cross sections

    Given a monoenergetic beam of photons, how are the interaction cross sections used to calculate a) the dose rate to a small volume of tissue, and b) the exposure rate. I assume this question references the below equations: \dot{D} = \theta ( \frac{μ}{ρ} )_{med} * E_{ab} \dot{X}...
  3. Telemachus

    Tensor algebra, divergence of cross product

    Hi there. I wanted to demonstrate this identity which I found in a book of continuum mechanics: ##curl \left ( \vec u \times \vec v \right )=div \left ( \vec u \otimes \vec v - \vec v \otimes \vec u \right ) ## I've tried by writting both sides on components, but I don't get the same, I'm...
  4. V

    Cross section in muon pair production from electron positron annihilat

    I have a question regarding the calculation of the cross section in muon pair production from electron positron annihilation. After some calculations the textbook comes to the conclusion that the differential cross section is approximately equal to: (1+cos(theta)^2)alpha^2/(4*s) where alpha...
  5. Greg Bernhardt

    What is the Definition and Properties of a Cross Product in Vector Algebra?

    Definition/Summary The cross product of two vectors \mathbf{A} and \mathbf{B} is a third vector (strictly, a pseudovector or axial vector) \mathbf{A}\times\mathbf{B} perpendicular to both of the original vectors, with magnitude equal to the product of their magnitudes times the (positive)...
  6. M

    Resistance Variable Cross Section

    Homework Statement The question asks for resistance R of a disk with radius r and fixed width w, whose cross sectional area is variable. Unlike in the picture below, the resistor is not connected to the circuit on the flat ends, but on the cylindrical sides. Homework Equations...
  7. F

    What does cross product of vectors actually mean?

    I understand that dot product of vectors means projecting one vector on to the other. But I don't understand what is the physical significance of a cross product? I have read that cross product gives the area of the parallelogram which has each of the vectors as its sides...but why do we want to...
  8. J

    Calculating Radar Cross Section for a Spherical Object in GHz Frequency

    How do I calculate radar cross section given the diameter of a spherical object and the radar's frequency in GHz? Thanks
  9. R

    Absorption cross sections of hydrogen ions

    hello, i need the values for the absorption cross sections of positive hydrogen ions for a specific set of wavelengths, Halpha to start with. At first i thought finding this on the web was easy, but turns out to not be trivial at all. If you can help me, i also need the (reliable) source...
  10. A

    Cross and dot product of two vectors in non-orthogonal coordinate

    Hi everyone, I have to find out how to do cross and dot product for two vectors in non-orthogonal coordinate system. thanks
  11. N

    Cross Plane 180 headers for GM LS V8

    I was looking into what cylinders need pairing to make a set 0f 180 headers for an LS V8 engine. When looking the pairings shown below. LS firing order 1-8-7-2-6-5-4-3 Passenger (L) side = 1 3 5 7. Driver side (R) 2 4 6 8 1-8-7-2-6-5-4-3 L-R-L-R-R-L-R-L for a 4-1 header I get. 1-7-6-4...
  12. 4

    What is the direction of the magnetic force on a charged particle?

    1. Here is the prompt: http://imgur.com/mfbPidG 2. F = qv x B 3. At first this seemed like a simple cross product problem, and it probably still is, but I'm really confused as to what "3.70E6 m/s/ in the (i+j+k)/sqrt(3) direction" means, so I don't know how to set up my problem anymore. Could...
  13. F

    Find specific reaction cross section in an ENDF file

    I'm trying to find specific reaction cross section 18O(p,n)18F in proton + O-18 TENDL (ENDF format). # p + 18O : (p,n) Total # Q-value =-2.51902E+00 # E-threshold= 3.64964E+00 # # energies = 45 # E xs 1.000E+00 0.00000E+00...
  14. B

    Proving A Result About the Cross Product

    Here is the claim I am trying to prove: Suppose we have two vectors \mathbf{r} and \mathbf{s}. I would like to show that there are only two directions in which the resultant vector of the cross product \mathbf{r} \times \mathbf{s} can point, parallel and antiparallel. How might one prove...
  15. C

    Maximizing Flow in a Rain Gutter: 3-sided vs Semicircular Cross Section

    A long piece of sheet metal w inches wide is to be bent into a SYMMETRIC form with three straight sides to make a rain gutter. A cross section is shown below. \_____/ The base is w-2x and the angled side lengths are both x with a theta between top horizontal. A. Determine dimensions that...
  16. karush

    MHB Volumn of parabola and line with perpendicular cross sections being a square.

    The base of a solid is the region bounded by the parabola y^2=4x, and the line x=2 . Each plane section perpendicular to the x-axis is square. (I assume this means the cross-section of the solid will be square) then we are not revolving but slicing. The volume of the solid is? (the ans is...
  17. S

    Calculating resultant torque using cross product

    1."In this exercise, you will be finding the resultant torque from the cross product of a lever arm with a force vector. The lever arm vector is A=2.0i+3.0j. The force vector is B=3.0i-4.0j. Find A x B B x A and 2A x 3B 2.My teacher has been sick the past few days so hasnt taught us...
  18. R

    The dot or cross product of two operators acting on a state

    If a system is made up by two subsystems, for example, the atom and the photon. and let's assume the state of the atoms is described by |\phi\rangle, while the state of the photons can be described by |n\rangle, The Kronecker product of the |\phi\rangle and |n\rangle can be used to describe the...
  19. M

    Radar Cross Section (RCS) problem

    As we know RCS is measure of how detectable an object is with a radar. But I don't understand one thing. If we take a sphere as an example, we can see that RCS is the largest in forward direction (forward scattering). If the sphere is to big (radius>>lambda), still this forward scattering is...
  20. C

    Rotation and translation of basis to remove cross terms

    So in our notes we are given a general quadratic equation in three dimensions of the form: Ax^2 + By^2 + Cz^2 + Dxy + Eyz + Fxz + Gx + Hy + Iz + J = 0 And then they say, by some rotation we can change this to the standard form: Ax^2 + By^2 + Cz^2 + J = 0 The lecturer said don't worry...
  21. N

    How do I produce a hole with a square cross section?

    What are three different ways that i can produce a hole with a square cross section in a plate with a thickness of at least 1"?
  22. Z

    Finding Cross Section Data for Tungsten, Rhenium, Osmium & Iridium

    Hi, I'm doing a project to see the feasibility of transmuting tungsten into platinum on a small scale (maximum output of 1 kg per month). However, some of the cross section data that I need seems to be hard to find. Now because I am new to this, I don't know if its because no body has...
  23. Safinaz

    Off-shell Particle Decay: Does Mass Affect Cross Section?

    Hi all, I think that the off shell decay dosn't decrease the decay cross section, I mean if a particle X decays into a jet pair has mass for example Mjj ~ 130 GeV, being X has mass M ~ 130 GeV so decay in resonance or on shell into jj or being MX even much greater ~ 2000 GeV , this...
  24. V

    Born-Bethe approximation for cross section

    Hi all I was trying to understand the Born-Bethe approximation related to cross sections for atomic and molecular collisions. All the stuffs that i got are explaining in complicated way which am not able to follow. Can anyone explain in simple terms what the theory explains? It will be of...
  25. M

    Perpendicular force from cross product

    Cross product is used to find the perpendicular vector of two vectors. If there is any two vectors in a plane then there is always a perpendicular vector to both of them. So in circular motion if the motion is horizontal then is there a perpendicular force to the object in circular motion?
  26. O

    Vectors - dot product and cross product?

    Vectors -- dot product and cross product? Hello may i know when to dot product and cross product?? both look to same to me..
  27. X

    Eikonal Approximation: Find total Scattering Cross Section

    Homework Statement Using the Eikonal approximation (1) Determine the expression for the total scattering cross section of a particle in a potential V(r) (2) Using this result, compute the total scattered cross section for the following potential. V(r)= \begin{cases} V_0, \text{for } r < a \\...
  28. P

    How Do Dot and Cross Products Differ in Describing Physical Phenomena?

    I am trying to understand the difference from a physical phenomena point of view, not just math. Surprisingly I think I got the cross product like in rotational momentum. You have the momentum vector and we have effective distance from the momentum vector R that needs to be perpendicular to the...
  29. J

    What does cross section area mean when dealing with stress/strain?

    What does "cross section area" mean when dealing with stress/strain? Homework Statement For clarification, here is an example problem: A circular steel wire 2 m long must stretch no more than 0.25 cm when a tensile force of 400 N is applied to each end of the wire. What minimum diameter is...
  30. J

    Cross product is cancellative?

    If u × v = u × w, so v = w ?
  31. B

    Electron-Muon Scattering Cross Section

    Hi, I am self-teaching Quantum Elctrodynamics, and have come across something which I do not understand. I would appreciate feedback from anyone on this specific issue from Atchison & Hey, "Guage Theories in Particle Physics" pg 238-239: In calculating the u-channel electron-muon...
  32. U

    What is the Impedance of a Cross Yagi Designed for RHCP?

    I'm designing a cross yagi as one component of a capstone project. The design I have right now is 3 elements per polarization, counting driven elements (total of 6 elements). I ran a quick 4nec2 simulation of a single polarization (3 elements) using center excitation on the driven element and...
  33. Z

    Higher dimensional cross products

    I've always heard that the cross product only exists in a well defined way for 3 and 7 dimensions. From my own reading I've found that a cross product in 3 dimensions is nothing more than the product of two quaternions with only pure imaginary components (that is, the real part is zero)...
  34. H

    Calculating the Cross Section for a Laser's Transition Rate Equations

    Homework Statement For a laser, assume single mode operation, only lifetime broadening due to A21 and A1. Write out the rate equations for the atomic densitions N1 and N2 and the flux \Phi. Then there's a diagram where there's 2 stats. Pump rate is P, stimulated emission between 1 and 2 is...
  35. S

    Calculate item from n-size cross product without creating product?

    Hi all, I'm trying to work out how I can get the set at specific index in a cross product without creating the whole product. For instance: I have array A of length 512 I also have a number that specifies how many times that array needs to be 'cross-producted' against itself. This gives me...
  36. R

    A question about the cross product as related to matrix multiplication

    I understand that the cross product, in lay mans terms doesn't exist unless we're in 3 dimensions. When you multiply two matrices together I have been told you get something similar. I hear that this is because a matrix can be treated as a vector. So if we are talking about measurable...
  37. A

    Cross products for unit vectors in other coordinate systems

    I am a bit confused often when I have to compute cross products in other coordinate systems (non-Cartesian), I can't seem to find any tables for cross products such as "phi X rho." in spherical I think that these unit vectors are considered to be "perpendicular," so would phi X rho just be "+/-...
  38. M

    Izod Impact test Cross Sectional Area

    Homework Statement Ok, so in a lab I was preforming Izod impact tests on notched polymer specimens. To complete my calculations I need to determine the correct cross-sectional area to use (Which is baffling me as the simple things usually do) The sample was loaded with the notch facing...
  39. T

    Cross Product Help: Homework Statement

    Homework Statement Given two vectors A⃗ = 4i + 7j and B⃗ = 5i − 2j , find the vector product A⃗ × B⃗ (expressed in unit vectors). Express your answer in terms of the unit vectors i, j, and k. Homework Equations The Attempt at a Solution I know how to cross and multiply them...
  40. A

    Finding the time when two stones cross paths

    Homework Statement Two stones are thrown simultaneously, one straight upward from the base of a cliff and the other straight downward from the top of the cliff. The height of the cliff is 6.69 m. The stones are thrown with the same speed of 9.97 m/s. After what time do the stones cross paths...
  41. anemone

    MHB Why did the chicken cross the road?

  42. JasonHathaway

    What is the meaning of line integrals?

    Hi everyone, What does \int \vec{f} × \vec{dl} mean? does it mean "The Line Integral of Vector Function on a positive curve L"? And are the following named correctly? \int \vec{f} . dl : Scalar Line Integral of a Vector Function \int udl : Line Integral of a Scalar Function
  43. M

    Calculus III; standard form of & angle to eliminate the cross produc

    Hi; I've been trying to solve the problem myself but i really don't what could be wrong; The problem says : Make the change of variables x=ucos−vsin y=usin+vcos where the angle 0<(phi)<2 is chosen in order to eliminate the cross product term in x^2+xy+y^2=6 Then find the standard form of...
  44. F

    Proton-proton inelastic cross section in MeV

    Dear Forum ： I'm looking for proton-proton inelastic cross section in MeV. There are lots of results in GeV, TeV. But I can not find the results in MeV in ENDF nor TENDL. https://www-nds.iaea.org/exfor/endf.htm ftp://ftp.nrg.eu/pub/www/talys/tendl2011/proton_html/proton.html Please advise...
  45. jdawg

    How do I solve the dot and cross product of 3i and jxk?

    Homework Statement The value of 3i(dot)(jxk) Homework Equations The Attempt at a Solution I know the answer is 3, but could someone please explain how to work this problem?
  46. D

    Confirmation of cross products

    I know that for the tangent unit vector ##t##, normal unit vector ##n##, and binormal unit vector ##b## that ##b=t\times n## and ##n=b\times t##. Is it true that ##t=n\times b##? **Edit** Ah! Yes it is. Nevermind. I should have known this was true.
  47. T

    Pythagorean theorem based on cross product.

    I was developing a pythagorean theorem proof based on the cross product of two vectors..Below is my final solution...My problem is I had to get around using the distance/magnitude formula because that is using the pythagorean theorem to prove the pythagorean theorem. But after searching, it may...
  48. S

    Help with volume by cross section question

    Homework Statement See the problem attached in this post. Homework Equations See the problem attached in this post. The Attempt at a Solution I set my limits of integration with respect to z axis and got an upper limit of 2 since that's the vertex point/height of the pyramid...
  49. andyrk

    Cross Cannizzaro and Intramolecular Cannizzaro

    While I was going through my course material of Aldehydes and Ketones, I came across Cannizzaro Reaction. It is of 3 types, namely: Self Cannizzaro, Cross Cannizzaro and Intramolecular Cannizzaro. I understood the Self one but was unable to understand the other two. In the Cross one,why is...
  50. F

    Hurricane Fluid flow, torque, cross product

    Homework Statement In 1993 the radius of Hurricane Emily was about 350 km. The wind speed near the center ("eye") of the hurricane, whose radius was about 30 km, reached about 200 km/h. As air swirled in from the rim of the hurricane toward the eye, its angular momentum remained roughly...
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