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. D

    Stokes theorem equivalent for cross product line integral

    "Stokes theorem" equivalent for cross product line integral Homework Statement I am aware that the vector path integral of a closed curve under certain conditions is equivalent to the flux of of the curl of the vector field through any surface bound by the closed path. In other words, Stokes...
  2. MathematicalPhysicist

    Hyperbolic Distance and double Cross Ratio.

    The question is as follows (by the way I'm asking here, cause the calculus and beyond forum seems to be primarily concerned with Calculus,DE, LA and AA): let f(z)=(2z+1)/(z+1) be an isometry of the hyperbolic plane H={z| Im(z)>0}. let l be a hyperbolic line in H which is invariatn under f...
  3. G

    Why Is Sin A Used in the Cross Product Equation F=qvBsinA?

    Homework Statement Just a general questions I don't understand. Why is it sin A in a cross product and not cos A? I don't understand it in the equation F=qvBsinA Homework Equations no The Attempt at a Solution ...
  4. F

    Calculating Work and Initial Displacement with Cross Product

    Hey guys, I normally don't use forums for help but I've been stuck on these questions for some time now and I just want to see if there's anyone out there who can set me in the right direction. These questions are from a grade 12 Calculus and Vectors class and they relate to the cross product...
  5. B

    What is the Difference Between Dot and Cross Products in Vector Calculations?

    dot product and cross product. i (think dot product is like eg (1,2,4).(2,4,5) = 30 and cross product is like eg(1,2,4)x(2,4,5)=2, 8, 20) but I am not sure... and is there an order like in a.bxc do u do bxc and then.a or do u go normal left to right. but if left to right what's the rule in when...
  6. R

    Photon-Proton Cross Section vs Electron-Photon

    why is the cross section of photon - proton less than the electron- photon cross section for the same photon energy??
  7. Y

    Does Linkage Matter in a Cross of Truebreeding Recessives?

    Just a simple question, if I got two genes with 2 recessive mutants, let say the wildtype A and B with mutants a and b. And I cross truebreeding mutants (AA bb, aa BB), linkage, in this situation, doesn't matter, I'll get Aa Bb anyway, am I right ?
  8. D

    Having trouble grasping the Cross Product

    I know how to compute it and how to use it in equations. I do not understand what is physically happening however. When you turn a disk to the right the angular momentum is the cross product of the forces so it goes perpendicular to them and away from you. To the left would be towards you...
  9. R

    Vector Cross Product: Calculating -i x i = 0?

    What is the cross product of -i x i? Is it negative 1 or is still just 0?
  10. I

    Calculating Cross Sections Using Intermediate Vector Boson Theory

    Would anyone know of any textbook that has explicit calculations of cross section using intermediate vector boson theory? I've looked in Perkins and Halzen+Martin but I do not see any in those texts.
  11. I

    Calculating Cross Section: Is (1-\gamma^5) Same as (1-\gamma_5)?

    Is there a difference between (1-\gamma^5) and (1-\gamma_5) ? I see the two used interchangeably when calculating cross section.
  12. G

    How can the vector cross product be calculated when only magnitudes are given?

    [b]1. Find axb: Given the magnitude of lal=3 and the magnitude of lbl=2. [b]2. Since I have the magnitudes, I thought maybe I could use the equation of axb=lal lbl sin theta. [b]3. I thought since I am trying to find axb that I could use 90 as the angle theta to find axb. I am...
  13. J

    Cross Product Fun: Deriving Statement 2 from Statement 1

    Homework Statement 1 (H_1 - H_2) \times \hat n = J_s 2 (H_1t - H_2t) = \hat n \times J_s How does one get from the first statement to the second statement? 3 H_{1t} - H_{2t} = J_s This is causing an interesting problem when I plug in numbers, I would have just left it with statement (3) but...
  14. C

    Calculusvolume with cross sections

    I need help please on a calculus problem. I am trying to teach myself and am doing fair. I am stuck on this though. Question:find the volume using CROSS SECTIONS that are squares. base is bounded by y = x + 1 y = x squared - 1 cross sections are squares perpendicular to the x axis I...
  15. C

    Best velocity to cross a rainy space

    I found this problem in the book Resnick and Halliday many years ago (1992) and I had it in my mind until 2005 or so when I was able to get some advance. "If you want to walk through a distance L in a rainy day, in order to get wet the little as possible what would you do, run as fast as...
  16. N

    How Do You Calculate Torque from Cross Product?

    Force F = (9.0 N) i hat + (-4.0 N) k hat acts on a pebble with position vector r = (3.00 m) j hat + (-1.0 m) k hat, relative to the origin.(a) What is the resulting torque acting on the pebble about the origin? ( N·m) i hat + ( N·m) j hat + ( N·m) k hat (b) What is the resulting torque...
  17. D

    Q: Can the vector product be factored out from an integral in electromagnetism?

    Hi. I have an integral of a cross product: \int a\times b(t)dt a does not depend on t. How can I move it outside? Is this legal: a\times\int b(t)dt ?
  18. H

    Vector Cross Product: Perpendicular Vectors lV_1 x V_2l

    If vectors V_1 and V_2 are perpendicular, lV_1 x V_2l =? I know that if they are parallel for vector cross product, they equal 0.
  19. N

    Cross Products: Solve For A Given B z-hat

    Homework Statement B = grad(A) Find A If one is given B z-hat Homework Equations The Attempt at a Solution What mathematical operation would I apply to solve this?
  20. T

    Finding Triangle Area using Cross Product

    Homework Statement Find the area of a triangle `PQR`, where `P=(0,4,4)`, `Q=(2,-6,-5)`, and `R=(-3,-5,6)` The Attempt at a Solution The vector PQ = (2, -10, -9) The vector PR = (-3, -9, 2) Using matrixes I set up something that looks like this... I J K 2 -10 -9 -3 -9...
  21. M

    (Neutron capture) cross section

    Cross section means the effective size of a nucleus for capturing a neutron, am I right? But what makes the cross sections for different nucleus different? I am a bit puzzled, why the cross section for Boron(for example) is so high?
  22. B

    Benchmark of high temperature cross section libraries in MCNP

    I need to use this libraries with confidence. Any articles that involves benchmarking of these cross sections?
  23. I

    Calculating Cross Section with 4-Fermi Interaction

    Hi all, I'm trying to teach myself high energy physics and was wondering if anyone knew a good reference site on calculating cross sections. I'm specifically trying to calculate the cross section for \nu _{\mu} + e^- \rightarrow \mu ^- + \nu_e using the 4-fermi interaction. Are there any good...
  24. A

    Vector Cross Product Formula in Spherical & Cylindrical Coordinates

    Hello all, it might be funny! but i am stuck to it! what is the vector cross product formula in spherical and cylindrical coordinates?! I know for Cartesian coordinate we have that nice looking determinant. but what about the other coordinates. I had looks to all the math books (like...
  25. P

    Solve Trihybrid Cross Problem: Phenotypic Ratio 27:9:9:9:3:3:3:1

    [SOLVED] Trihybrid Cross Problem Hi, I need help trying to figure out how to solve this question: Assume that in rabbits there are three different independently assorting autosomal loci that affect coat color. A colorless-pigment precursor V is converted to a colorless precursor W by action...
  26. T

    Two vectors are parallel if their cross product is 0?

    the question is: u = 9i-6j and v = 5i+bj for what value of b would u-v point in the same direction as w = 7i-3j? can anyone help me get started on this problem, I am not looking for answers just a little bit of help because I'm confused.. thanks
  27. K

    Geometric algebra cross product

    geometric algebra cross product -------------------------------------------------------------------------------- Homework Statement [/b] my text (Geometric Algebra for Physicists, by Doran and Lasenby), p. 69, deals with rotating frame {fsubk} (I assume in 3D) d/dt (fsubk) = omega X...
  28. K

    Geometric algebra cross product

    Homework Statement [/b] my text (Geometric Algebra for Physicists, by Doran and Lasenby), p. 69, deals with rotating frame {fsubk} (I assume in 3D) d/dt (fsubk) = omega X fsubk omega being angular velocity then omega X fsubk = (-I omega) dot fsubk = fsubk dot (I omega), where...
  29. L

    Differential Cross Section for scattering by Hard Sphere

    Problem Determine the differential and total cross sections for scattering from a "hard sphere" of radius R ("hard" means impenetrable). Relevant Formulae \sigma (\Omega) d \Omega = \frac{number \ of \ particles \ scattered \ into \ solid \ angle \ per \ unit \ time}{incident \ intensity}...
  30. F

    Vector, cross product, and integral

    [SOLVED] Vector, cross product, and integral Homework Statement Evaluate: {\int \textbf{F} \times \texttt{d}\textbf{v}}. \textbf{F} and \textbf{v} are both vector fields in \mathbb{R}^3 Homework Equations \texttt{d}\textbf{v} = (\nabla \otimes \textbf{v} ) \texttt{d}\textbf{r} The Attempt...
  31. M

    Where can I find step-by-step calculus for QFT processes online?

    Im currently studying different kinds of processes in QFT. Does somebody know where to find all the calculus done step by step on the web. It will be very helpfull. thanks in advance, Marco.
  32. tony873004

    Vectors: cross product question

    If a, b, and c are vectors, and a=b x c, and a and c are known, how do I solve for b? b=a/c ? I don't think we've covered diving vectors, and since the cross-product is a special case of multiplying vectors (as opposed to dot product), I'm not sure this is allowed anyway. I'm trying to...
  33. T

    Cross product and dot product scalars

    Homework Statement If d1 = 4i - 10j + 2k and d2 = 9i - 10j + 6k, then what is (d1 + d2) · (d1 × 4d2)? Homework Equations Know how to do the cross product and dot product The Attempt at a Solution For the answer i got 9.6i + 56j -127.68k. How do i express that as a scalar for an...
  34. B

    Derivative of the cross and dot product

    Homework Statement If you have two functions dependent on t, A(t) and B(t). Prove their derivatives are as follows: d(A (dot) B) / dt = [A (dot) (dB)/(d(t)] + [d(A)/d(t) (dot) B] {Where "(dot)" acts as the dot product} d(A x B) / dt = [A x (dB)/(d(t)] + [d(A)/d(t) x B]...
  35. T

    S- and P-Wave Cross Section Explained

    What does it mean when they say s wave cross section, p wave cross section .. ?
  36. P

    What is the Derivative of a Cross Product?

    [SOLVED] derivative of a cross product Homework Statement In some lecture notes I'm reading they jump straight from \frac{d}{d\mathbf{r}}( \frac{m}{2} |\mathbf{\omega}\times\mathbf{r}|^2) to \mathbf{r}\omega^2-\mathbf{\omega}(\mathbf{\omega}.\mathbf{r}) Homework Equations The...
  37. I

    Understanding the Normalization of Cross Products: A Brief Explanation

    [SOLVED] normalizing a cross product Homework Statement How does normalizing (T(t) x T'(t)) equal ||T'(t)||? Homework Equations r'(t) x r''(t) = ||r'(t)||^2·(T(t) x T'(t)) ||r'(t) x r''(t)|| = ||r'(t)||^2·||T'(t)|| The Attempt at a Solution This doesn't bode well with me...
  38. I

    Proof of r'(t) x r''(t) = ||r'(t)||^2 · (T(t) x T'(t))

    Homework Statement We know that T(t) = r'(t)/||r'(t)||, or equivalently, r'(t) = ||r'(t)||·T(t). Differentiate this equation to find r''(t), then show that r'(t) x r''(t) = ||r'(t)||^2 · (T(t) x T'(t)). Homework Equations r''(t) = ||r'(t)||'·T(t) + T'(t)·||r'(t)|| The Attempt at...
  39. J

    What is the Cross Section of a Hydrogen Atom in Thermal Equilibrium at 6000K?

    Homework Statement I've been asked to find the cross section of a hydrogen atom in thermal equalibrum at 6000K for a photon which induces a transition from the ground state to the first excited state. The density of states for n=2 is 4x the density of states for n=1 i.e. g(E2) = 4*g(E1)...
  40. D

    Pythia and differential cross sections

    Dear Users, I would like to ask you how can I plot d_sigma/d_Pt graph for proton proton collisions using pythia event generator. I am also using root macro which plot d_N/d_Pt graph for pion and I have also attached this for you. I would be garetful if you could tell me how can I convert this...
  41. J

    Vector Cross Product: R4 Vectors & Permutation Symbol

    Is there such a thing as a cross product for R4 vectors? Can you use the permutation symbol to express it in the same way that it can be expressed in R3? Would the correct way to write it be: e _{i,j,k,l} u _{j} v _{k}?
  42. M

    How to Tackle Difficult Online Homework Assignments

    Homework Statement A force F = (5 i - 1 j) N acts on a particle that undergoes a displacement r = (2 i + j) m. (a) Find the work done by the force on the particle. (Calculate all numerical answers to three significant figures.) (b) What is the angle between F and r? * the problem required us...
  43. P

    Mean free path and collisional cross section in Na due to impurities

    Let's say that we have Na at room temperature. The concentration of Na becomes plus one percent due to impurities. I'm interested in finding the mean free path and collisional cross section due to these impurities. I'm not sure on how Matheissen's rule could be applied, if we don't know what the...
  44. A

    Proving a subset of a cartesion cross product

    Homework Statement A, B, C and D are sets if A x B is a subset of C x D then A is a subset of C and B is a subset of D. The Attempt at a Solution My attempt by contraposition. Assume A is not a subset of C or B is not a subset of D. There exists an 'a' which is an element of A...
  45. G

    Cross Section Large Hadron Collider

    Homework Statement b) The Large Hadron Collider (LHC), a 14 TeV proton-proton collider, will produce about a million Z0 per year. Explain why the cross section of such a process can be approximately written as: d\sigma / d\Omega = F_{q/p}(X_{1})F_{q'/p}(X_{2})d\sigma '(qq' \rightarrow...
  46. K

    Solving Dot & Cross Product Equations: Vector Positioning

    Q:Given non-zero vectors u and v, find a vector x such that both equalitites x dot u=|u|, and x cross u = v hold. What should be the mutual position of the given vectors u and v in space, so that the problem has a solution? What I've got so far: Setting x = au + b(u cross v) I have that...
  47. N

    Differential cross section w.r.t rapidity

    I'm extracting data from a Monte Carlo sim. and i need to extract the differential cross-sections of the resultant protons and neutrons in momentum and rapidity space. ie \frac{d\sigma}{dy} ; \frac{d\sigma}{dp} and \frac{d^2\sigma}{dydp} where I know the values of y and p...
  48. H

    How to find neutron capture and fission cross section

    I'm writing a paper on Thorium utilization in nuclear reactors. In this connection I'm looking for figures which describe the neutron capture and neutron fission cross sections over a wide energy range (not only thermal). There are probably some online resources unbeknown to me, any hints?
  49. S

    Calculating Scattering Cross Sections

    Homework Statement A beam of \alpha-particles, of kinetic energy 5.3 MeV and intensity 10^{4} particle/sec, is incident normally on gold foil with thinckness 1 x 10^{-5} cm. (The density, atomic weight and atomic number of gold are 19.3 g/cm, 197 and 79 respectively.) A particle counter of...
  50. R

    What are the possible directions for cross products involving three vectors?

    Homework Statement Sketch a 3-dimensional picture showing the horizontal plane, a point P on the plane, a vertical line through P, and three vectors at P: vector A points vertically upward; vector B points toward the east; vector C points toward the south. Now determine the cross...
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