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. L

    Where can I find detailed derivations for relativistic scattering calculations?

    I am looking for notes or a book that covers nicely the calculations for relativistic scatterings (Bhabba, Compton, pair annihilation, Moller, etc. ) Most QFT books, after explaining Feynman diagrams do not give too much details when it comes to cross section and decay rates. Often they put...
  2. Q

    What is the formula for the differential cross section and macro cross section?

    hello , can anyone give the formula of the differential cross section and the macro cross section because in each web i see a different notation thank you
  3. F

    Vector geometry: Proof of a trapezium and cross and dot product help

    Homework Statement #1 Given that the angle between the vectors a and b is 2Pi/3 and |a|=3 and |b|=4 calculate: (axb)^2 [(2a+b)x(a+2b)]^2 #2 Given three unit vectors, a, b, c such that a+b+c=0 find (a dot b) + (b dot c) + (c dot a) #3 Given AB=a+2b BC=-4a-b CD= -5a-3b...
  4. jtbell

    Why did the salmon cross the road?

    Because it wanted to get away from the new PF member who called it his favorite fish! https://www.youtube.com/watch?v=2fr9bY0_JB8
  5. P

    Algebraic vector problems (planes, cross products etc)

    Homework Statement 1. A vector u is given by u = λa + μb, where λ, μ are elements of ℝ. Calculate axu and bxu and show that: [(b χ u).n]/[(b χ a).n] = λ and [(a χ u).n]/[(a χ b).n] = μ (In any circumstance when I have omitted the underlining it is for convenience purposes, a, b...
  6. P

    Why is the second cross section preferred for designing a beam?

    Consider the cross section of two beams of same material as shown in the file attached. The area moment of inertia I about the central axis is equal for both the c/s. I have calculated it. Can somebody explain why the second c/s (2 in the figure ) is preferred for the design?
  7. L

    The effect of cross validation on correlation coefficient

    I have two variables where the regression line is just the mean as a constant. As such, the correlation is zero. However, when I perform k-fold cross validation (in Weka) this becomes non-zero. I have no idea why this is. The regression line for whatever the test set is will always be a...
  8. J

    Cross Polarizers with a wave plate retardation

    Homework Statement "Consider a wave plate with a retardation τ=(η_0-n_e)*w*L/c. Show that when it is placed between crossed polarizers with its optical axis at an angle of θ with respect to the polarizer axis, the transmitted intensity is given by: I_out/I_in= (sin^2(2θ)(sin^2(τ/2)) In...
  9. T

    Confusing index notation involving grad of w cross r

    Homework Statement consider the position vector expressed in terms of its cartesian components, r=xiei. Let w=wjej be a fixed vector whose components wj are constants that do not depend on the xi, so that δwj/δxi = 0 Homework Equations I am trying to evaluate ∇((wXr)^2) The...
  10. H

    Dot and Cross Product from Rotation Matrix

    I'm just learning this Latex(sic) formatting, so it's not ideal. I was trying to explore the geometrical significance of the cross product when I happened upon an interesting observation. I've seen things like this before, but never had time to really examine them. I define two vectors...
  11. C

    Integral of differential cross section over solid angle

    Homework Statement Find σ , the differential cross section, starting from the expression below and integrating over solid angle Ω Homework Equations dσ/dΩ = r2sin2θ The Attempt at a Solution dσ = r2sin2θ dΩ I remember that dΩ = sinθ dθ dμ and doing the μ integral from 0...
  12. Calculuser

    How Can You Prove the Cross Product in Vector Mathematics?

    Hi, I was studying Maths the subject of Vector and found two important rule which are "dot" and "cross" product. I proved the first by myself with the (c^{2}= a^{2}+b^{2}-2.\|a\|.\|b\|.cosθ) However, the I couldn't make out how to prove the other one. I've been so thoughtful about it and need...
  13. B

    Proving a relation between cross and dot products

    Another vector identity I have been trying to prove. My textbook lists this identity in "properties of cross products" without proving it. I have been trying to prove it, withou much luck, so some insight is appreciated. u \times (v \times w) = (u \cdot w)v - (u \cdot v)w Thanks! BiP
  14. S

    Vector cross product with coefficients

    Anyone know how would I simplify a cross product where the two vectors have coefficients? For example (x/(y^3))\bar{r} X (x/(y))\bar{L} Thanks!
  15. P

    Neutron capture cross section of tritium is zero

    I wish to verify a couple of assertions. From the NNDC and other references, it appears that the neutron capture cross section of 3H (Tritium) is zero to a first approximation. This holds true for all neutron energies, including cold neutrons. These statements are equivalent to asserting that 4H...
  16. E

    List of all the cross and dot products in physics?

    the calculation of many quantities involve cross and dot products in their formulae. For cross products, i only know of three: lorentz force, angular momenta and torque. For dot products, i only know of one: work done im hoping to add more to my list. Can you guys help me include other...
  17. J

    Calculating Cross Sections from Events + Luminosity

    Hello, How can I convert the number of events + the luminosity in a cross section? I think this must be trivial... thanks..
  18. C

    Given one cross product, find another cross product

    Homework Statement Calculate the cross product assuming that u X w = <-7,1,8> Find (-3u + 4w) X w = ? Homework Equations I'm not sure. I know you have to relate the cross product to something inorder to find what u and w are, but don't know what equations to use. The Attempt at a...
  19. S

    Question regarding cross products and determinants

    I understand how to calculate a vector cross product. I also understand that in order to calculate a vector cross product we are calculating the determinant of a 3 x 3 matrix. I guess I have a few questions. 1)How did mathematicians or physicists discover how to calculate the determinant...
  20. K

    Why is Torque the Cross Product Between r and F?

    Examine T= r x F (cross product), where |T|=|r||F| sin t, where t is the angle between r and F The intuitive idea of torque (let's only consider torque about the pivot for now) is that the stronger the force or the further away you are from the pivot point, the more the object will TEND to...
  21. M

    Cross Product of Two Vectors

    1. See attached image please! 2. For part (a), I applied the cross product and got (-6i - 2k) for (\vec{A}x\vec{B}. I got (6i + 2k) for (\vec{B} x \vec{A}). For part (b), \vec{C} was simply (-6i - 2k) - (6i + 2k) = (-12i -4k). For part (c), the magnitude of \vec{C} was simply 12.65 and for the...
  22. J

    Two questions on vectors, regarding dot and cross product?

    Homework Statement 1. Suppose that u + v + w = 0. Show that u x v = v x w = w x u. What is the geometric interpretation of this result? (Note: The interpretation should explain both the length and the direction). 2. Let v1, v2, and v be three mutually orthogonal vectors in space. Use the...
  23. D

    Cross Product Magnitude for Triangle Area

    Homework Statement So I have several problems on my homework which deal with the application of cross product and its magnitude to find areas. I know how to do cross product, and I know how to find the magnitude, however, no matter how many times I try to calculate it, I get the wrong...
  24. C

    Proving trig identities with dot and cross products

    Homework Statement The two vectors a and b lie in the xy plane and make angles α and β with the x axis. a)By evaluating a • b in two ways (Namely a •b = abcos(θ) and a • b = a1b1+a2b2) prove the well-known trig identity cos(α-β)=cos(α)cos(β)+sin(α)sin(β) b)By similarly evaluating...
  25. F

    Spin statistic terms in absorption cross section

    'Ello, I have a question regarding the results in this paper (and another which I will mention later) http://arxiv.org/abs/hep-ph/0212199 Now, I'm not so concerned about the 'braney' bit, but more their definition of the cross section in Eqn. (46). They have included the usual (2j+1)...
  26. T

    Understanding Cross Product: Vector Product and Angle Separation Explained

    I have two problems: Homework Statement In general, what can be said about the vector product x×(x×y) The Attempt at a Solution I thought the result of this would be parallel to y. However the answer suggests it is orthogonal to x. Can anyone explain how I could approach this...
  27. B

    Can you do the Cross Product Backwards?

    I was doing a question in a test involving the system of moments , you are given 2 force vectors and two points respectively . And you must find a third point and force to make the 3 moments in equilibrium . So I did the cross product with the first force vector and its point and then with the...
  28. A

    From matrix element to hadronic cross section

    Hello, currently I work on 2->3 scattering process. So there exist five external momenta and in my case 5 different Feynman diagrams, for which I have already calculated the full matrix element. The matrix element is a function of various scalar products of the four-momenta. This scattering...
  29. N

    More volume of a washer cross section(integration)

    Homework Statement Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Homework Equations y = x^2, x = y^2 about y = -1 The Attempt at a Solution I tried using both cylindrical and washer methods - but for...
  30. N

    Volume of the solid using a cylindrical cross section

    Homework Statement Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Homework Equations y = \sqrt{x-1} , y = 0, x = 5; about y = 3 The Attempt at a Solution I already completed graphing it, but not really sure how...
  31. haael

    Cross product and matrix multiplication

    Suppose that we have a cross-product of vectors. a × b = c Now suppose that we have an orthogonal matrix M. Is it true that (M a) × (M b) = M c ? My intuition is that here we are moving to another coordinate system and performing a cross product in this new system. I can't find an...
  32. noir1993

    Reconcile Geometric Form of Cross Product with Algebric Form

    Basically, we have to prove that A X B is equal to ABsinθ Now a crucial step towards the proof is proving that (AXB).(AXB) is equal to (AB)2 - (A.B)2 After that it is fairly simple. But unfortunately, I can not prove the identity. I've tried expanding it into components but things are...
  33. S

    Calculate Dead Load of Beam w/ Solid Square Cross Section

    Homework Statement A beam has a solid square cross section of 100mm and is simply supported by two supports 3m apart. Calculate the dead load that can be safely supported when applied to the middle of the beam. Homework Equations Solid square cross section of beam: 100mm Material...
  34. W

    Why the photoelectric cross section decreases with the energy of the photon?

    the higher the energy of the photon, the more powerful it can ionize an atom but why then the absorption cross section decreases with the photon energy?
  35. K

    Calculate throw angle to have the curve cross a certain point

    Hello, I'm not sure if this is the right section because this is somewhat of a hybrid of math and physics. Say I have a ball in 3D space, its initial position and its' initial acceleration. Furthermore I have another point in 3D space which I want the ball to pass through, if possible. The...
  36. W

    How is the scattering cross section measured?

    a basic problem but i have no idea how to measure it
  37. Philosophaie

    Is A Cross B Equal to Zero a Test for Orthogonal Cases?

    A cross B equals zero is a test for orthogonal cases. If AxB=0 then A is perpendicular to B.
  38. M

    What are the units for the two photon LIF signal?

    Hello. I was hoping someone could help me understand some units. In several papers, I have seen the two photon LIF signal written as: S = n*(Ω/4π)*T*G*σ*(E/hv)^2*η*a where the units are n (density of measured atom): #/cm3 Ω/4π (solid angle fraction): unitless T (optical transmission...
  39. H

    Angle between 2 vectors given dot product and cross product

    Homework Statement A dot B=0.707m^2, A cross B=4.950m^2 k^. If |A|=2.500m and B makes an angle of 135° with the positive x-axis, what are A and B in component form? Homework Equations A*B = |A||B|cos(θ) A X B = |A||B|sin(θ)@RHR The Attempt at a Solution I have no prior physics...
  40. J

    How do particle scattering cross sections scale with energy in colliders?

    How do particle scattering cross sections scale with energy in colliders? Particularly photons, electrons, protons, and gold or lead nucleii? (If necessary, break this into four separate questions.) It is stated that due to the Heisenberg uncertainty principle, it takes more energy to...
  41. D

    Why sine is used for cross product and cosine for dot product?

    While we calculate cross product of two vectors let A and B we write ABsinθ. And while we calculate dot product of them we write ABcosθ. Why particularly we use sinθ for cross product and cosθ for dot product.Is there any physical reason why we choose sine for cross product and cosine for...
  42. m4r35n357

    Boyer-Lindquist Cooridinates - incorrect sign on cross term?

    OK, I realize I am probably on a hiding to nothing here, but please bear with me for now, I have tested my calculations so carefully that I am totally convinced that I have found an error in two published accounts of the BL line element . . . The first is Visser, equation (57)...
  43. M

    Volume of cross sections using isosceles right triangle

    Homework Statement The area is bounded by the equation y=x^2, x-axis and the line x=3 and is perpendicular to the x axis Homework Equations A=1/2bh Height=Base The Attempt at a Solution A=1/2B^2 V=1/2B^2 from 0 to 3 V=1/2 B^3/3 from 0 to 3 V=B^3/6 from 0 to 3 V=27/6 please...
  44. M

    Volume of cross sections using rectangles

    Homework Statement The area bounded by y=√x, the x-axis and the line x=9 and is perpendicular to the x axis. find the volume of the cross section using rectangle with the h=1/2b Homework Equations The Attempt at a Solution I just want to know if I'm correct or on the right track...
  45. E

    Finding volume by using cross section?

    Homework Statement The only given data is that the cross section is 1m^2, the shape is circular (like a cut wire/rod) and i have to find the volume. Homework Equations from what I've searched, i found the equation: but i have no idea what to do with it, i still haven't learned it at...
  46. P

    What is the difference between dot product and cross product in physics?

    Why is dot product given by a*b cosθ whereas cross product ab sinθ.
  47. M

    Rectangle volume using cross sections

    Homework Statement Cross sections are perpendicular to the x-axis and rectangle has the h=1/2b. The region is bounded by the area y=x^2, x-axis and the line x=3 Homework Equations The Attempt at a Solution A=BH A=B(1/2B) A=3/2B V=3/2(x^2-3) just wondering if this is correct...
  48. M

    Volume of a square using cross section

    Homework Statement What is the volume if the area bounded by y=x^2 and y=9 and the cross sections are perpendicular to the y axis Homework Equations The Attempt at a Solution I have no idea
  49. G

    Proving that cross partials in R^2 are equal if

    There is a theorem stating the following: Let f be defined in a neighborhood of (x0, y0) in R^2. Suppose f has partial derivatives f_1, f_2, f_12, and f_21 in this neighborhood and that the cross partials f_12 and f_21 are continuous at (x0, y0). Then the cross partials f_12 and f_21 are...
  50. R

    Is there a difference between cross section and scattering cross section?

    I'm just wondering what the difference is between a cross section and a scattering cross section? Or is there any? I can't seem to find anywhere that clears it up, in fact there's a whole section on scattering cross sections in Kibble and Berkshire but they don't define it once :P
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