Cross Definition and 1000 Threads

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. P

    Cross Section Difference Bhabha Scattering and Muon Pair Production

    Hello, how do the angular distributions of Bhabha Scattering e^+ e^- \Rightarrow e^+ e^- and Muon pair production e+ e- \Rightarrow \mu^+ \mu^- differ? Regards, Phileas Fogg
  2. Saladsamurai

    Dude. How do you Uncross a cross product?

    Homework Statement If I have \vec{v}=\vec{\omega}\times\vec{r} how do I solve for omega? How do I "cross divide"? Scalar operations are easier, I know. But how do you do this vectorially?
  3. E

    Proof this cross product property

    Homework Statement Show that : || a x b||^2 = ||a||^2||b||^2 - (a . b)^2Homework Equations The Attempt at a Solution I don't know where to start off
  4. X

    The cross product and dot product of vectors

    http://img297.imageshack.us/img297/2527/physicsin9.jpg i've been working with the AxB in the first one, and found that |A||B|sin(theta) = A x B, and i thought i had found my theta to be 1 degree, but i don't believe that's right. also, when i attempted to do the dot product with the C vector...
  5. L

    EM radiation cross over materials

    Anybody knows if there is a rule for EM radiation cross over materials ? The wavelenght in comparison the size (or structure) of molecule is determinant ? Ex. why infrared pass through the concrete but not metalics ? Thank you.
  6. L

    Deflection of a solid body with different cross sectional areas

    Hello! I want to know the deflection at certain points in a solid body with different cross sectional areas. A force (F) is applied at one of the different sections. I want to know the deflection where the force is applied and what the deflection is on the other parts of the body. Im going...
  7. K

    Approximate cross section calculations

    Hello Ive come across some approximate cross section formulas during a course of particle physics. And in a reaction like A + B --> R --> C + D the cross section should be something like \sigma = K\frac{\Gamma_R^{AB}\Gamma_R^{CD}}{(s-m_R^2)^2+m_R^2\Gamma_R^2} Where K is a constant (depending...
  8. Lisa!

    MATLAB Draw Thomson cross section in polar plot by matlab

    Well I'm supposed to draw Thomson cross section in polar plot by MATLAB software. Have I done it right? I mean does this figure that I got seem to be in polar plot or not? t = 0:.01:2*pi; r = 2.8179e-13 x = t,0.5*power(r,2)*(1+power(cos(t),2)) polar(t,x) Thanks
  9. M

    Can Geodesics Cross? - Exploring GR Proofs with Maki

    Hi, I am currently doing a course in GR and have just gone over a proof of the focusing theorem.. now this relied on the fact that geodesics do not cross. But I could not see clearly the contradiction if geodesics did happen to cross? any help would be greatly appreciated. Maki :smile:
  10. S

    Understanding Continuity in the Cross Product Function

    [b]1. Show that the cross product is a continuous function. The Attempt at a Solution I have tried to apply the definition of continuity: find a delta such that |x-y|< delta implies |f(x)-f(y)|< epsilon but I'm having trouble making sense of what |x-y| is. As I see it, x is a pairs of...
  11. E

    Finding the Cross Product of A and B: A Puzzling Answer?

    Homework Statement A = -3i + 4j and B = 2i + 3j so I want to find AxB Homework Equations The Attempt at a Solution what I got is -9k + 8k, which is -k but the answer solution says it's -17k ?
  12. Y

    What is cross product of two complex numbers?

    Let U=a+jb, V=c+jd. What is U X V? Where "X" is the cross product. Can you explain?
  13. M

    Cross product between vecter and tensor

    Homework Statement Just wanted to ask what's the definition of the cross product between a vector and a range two tensor The Attempt at a Solution (x \times \hat{T})_{i\beta}=\epsilon_{ijk} x_j T_{k\beta}
  14. S

    A few questions relating to the cross product

    Ug. My first try at this and my whole post was deleted. Here goes again :) Homework Statement i) Two cities on the surface of the Earth are represented by position vectors that connect the location of each city to the centre of the earth. Assuming that the centre of the Earth is assigned...
  15. J

    Differential cross section/simple integral

    At least it should be a simple integral... Homework Statement The whole text is here- http://i35.tinypic.com/2nisnp.jpg Basically (I think) I need to integrate the differential over all angles theta and phi, and get sigma(naught) back out. Homework Equations given in pic...
  16. R

    Cross slip problem in f.c.c crystal

    Homework Statement Because the book gives me little information about the cross slip. So I can't handle the basic problem below. I appreciate that you can give me some hints or suggestion. An f.c.c crystal is deforming by motion of disslocations on the (a/2)[101](11-1) (I use minus instead of...
  17. S

    When to us dot versus cross product

    Hi folks, When you're squaring the sum of two vectors (v_1 + v_2)^2, why is it that it comes out as v_1 dot v_1 plus 2*v_1 dot v_2 plus v_2 dot v_2? Why do we use the dot product here instead of cross product? I understand that dot product is the multiplication of their parallel...
  18. F

    Bending a laser beam's cross section possible?

    So here's a crazy question...I was trying to think it through and have come up with nothing. Is it possible to bend a laser beam's cross section? For instance, if you are using a diode bar (which has a beam cross section resembling a line) is there a simple way to bend it into a...
  19. RyanSchw

    Curvature, More of a cross product question really.

    I've been using various methods of finding curvature, and using the forumla K=\frac{||\vec{r}'X \vec{r}''||}{||\vec{r}'||^3} I took the cross product of my two vectors and came up with (just assume this is correct, if my question isn't answered i'll post all related work)...
  20. A

    Finding Components of Cross Product for Vectors A and B

    Homework Statement Vector A = 3.5i + 1.8j and vector B = 1.7i + 4.8j . Find the components of A x B: Homework Equations AxB = AB sin(theta) The Attempt at a Solution Since vector A=3.5i+1.8j and B=1.7i+4.8j, I translated that into vectors. So, A is 3.94 @ 27.77*, and B is 5.09 @...
  21. S

    . Air and water in a cross flow heat exchanger. The fluids do not come

    Hi, I am trying to do a cross flow analysis in FLUENT. Air and water in a cross flow heat exchanger. The fluids do not come in contact. I have modeled and meshed the geometry in GAMBIT. Could someone pls help me with the steps in FLUENT as to how to assign different fluid properties for...
  22. P

    Abuse of Notation - Cross Product

    http://en.wikipedia.org/wiki/Abuse_of_notation I don't want this thread to go too long. But can someone quickly explain to be how the Determinent method of evaluating the Cross Product is an "abuse". I cannot quite seem to grasp their explanation...
  23. J

    Cross Product: Simple Cross Product

    (This is part of a much larger problem) Homework Statement Find \hat{r} \times \hat{z} \times \hat{y} Homework Equations x=rsin(\theta)cos(\phi), y=rsin(\theta)sin(\phi),z=rcos(\theta) (cartesian->spherical) The Attempt at a Solution I decided...
  24. T

    How to Perform a Cross Product on Polar Coordinates?

    I would like to know how to perform a cross product on polar coordinates. Thank You
  25. J

    Area of a triangle in 3 space using cross product

    Hi all, I have a general question. When calculating the area of a triangle in 3 space, one applies the formula 1/2||axb||. Given three vertices, a,b,c...does it matter which vectors we choose to use (ab, bc, ac) as our a b vectors? Thanks!
  26. M

    Can anyone describe to me the difference between dot product and cross product?

    I guess one of them is scalor and one of them is vector, but what is the REAL DIFFERENCE between them? gracias
  27. A

    Vof solid with circular base&right isoceloes perpendicular cross sections

    [[URGENT]]Vof solid with circular base&right isoceloes perpendicular cross sections Homework Statement so there is a circle described by the equation x^2+y^2=1 with right isosceles triangles perpendicular to it. each of the triangles is touching the circle with one of its LEGS, with the 90...
  28. B

    Medical Can Laser Eye Surgery Correct Cross Eyes in Adults?

    Can laser eye surgery/anything fix cross eyes? 2 of my friends are cross-eyed and they're adults ty
  29. P

    I proving that the cross product of 2 countable sets is countable.

    Statement to prove: If A and B are countable sets, prove A x B is countable. My work so far: I've thought of 2 ways to approach proving this. (1) I read that "Every subset of a countable set is again countable." So my first choice of proving this would be to state that it's given A and B...
  30. C

    Area of a Parallelogram with out cross products

    Homework Statement given the vertices: (0,0) (3,1) (2,3) (5,4) Homework Equations solving without cross products and with mathematica if available The Attempt at a Solution Te1=[3] [1] Te2=[2] [3] [det[Ay]] ________ [det[A]] get you the solution...
  31. F

    How to Find \vec{b} in a Cross Product Problem?

    I have a question about solving a problem involving a cross product. I understand how to find \vec{a} X \vec{b} = \vec{c}, but if \vec{a} and \vec{c} are given how do I find \vec{b}? Is there something I can do analogous to c/a =b? I've been reviewing my old calc III and linear algebra notes...
  32. B

    Cross product vs dot product headache

    Homework Statement Show (A x B) dot (C x D) in terms of dot products only. Homework Equations A x B = ABsin(theta) A dot B = AB cos (theta) The Attempt at a Solution Subbing both those formulas into the top I got [ABsin(AtoB) times CDsin(CtoD) ] cos(between the two resultant...
  33. P

    Finding Orthogonal Vectors in R^5 without Cross Product

    Homework Statement Given vectors a=(1,-1,0,2,1) b=(3,1,-2,-1,0) and c=(1,5,2,4,-4), which are mutually orthogonal, find a system of linear equations that a vector x must satisfy so it is orthogonal to a, b, and c.Homework Equations None I think. The Attempt at a Solution This is part A of...
  34. M

    Find the Coordinates of Point B using Cross Product

    Homework Statement Point A is at (0,3,0), D(0, 0, 3), C(4, 0, 0) and B(x,y,z). The bar AB is 7.09 m long and is perpendicular to the bars AC and AD. Use the cross product to determine the coordinates of x, y, and z. Homework Equations The cross product matrix thing... The Attempt at a...
  35. D

    Is the Result of a Cross Product in R^3 a Vector in R^3?

    Hi everyone... I just wanted to know if you compute a cross product of two vectors in R^3, do you get a vector in R^3 or an actual value(say both vectors have actually values)... Another question. I did this in class but I wasn't sure how it would work. Let say I have a metrix 2x2. how do...
  36. N

    How to determine the darcy friction factor for irregular cross section ducts

    How to determine the darcy friction factor for irregular cross section tunnels hi, I needed to calculate the f value for tunnels with these cross section area but I am not sure what are method available to calculate these shapes. Two of those cross section areas are already provided as...
  37. D

    Vector Cross Product (with Right Triangle)

    Homework Statement For the vectors in the figure below, with a = 8, b = 7, c = sqrt(113), give the magnitude and direction of the following cross products. (See attachment for figure/right triangle). (a) a x b (b) a x c (c) b x c Homework Equations \vec{A} \cdot...
  38. R

    Moment of Inertia / Section Modulus for a cruciform (rectangular cross)

    Hi, I'm trying to find a formula to help me find either the Moment of Inertia for a cruciform (rectangular cross) or better yet, its Section Modulus (S). Please see attached image.
  39. M

    The logic behind the cross product with units

    The cross product equals to the area of the parallelogram defined by the two vectors (at least in R^3). So if working on vectors which units v_1 = (1,2,3)m v_2 = (3,4,5)m it correctly returns the according area. However, if used to get a vector perpendicular to each of the vectors the...
  40. T

    How to Determine Neutron Interaction Time for a Given Nucleus?

    Suppose we consider a beam of neutrons incident upon a thin target with an intensity of 10^12 neutrons/(cm^2.s). Suppose further that the total cross section for the nuclei in this target is 4 b. Using this information, determine how long one would have to wait, on the average, for a given...
  41. P

    Path Integral of F = (x, y2, 2z) from a to b - Calculating Line Integrals

    Homework Statement For F = (x, y2, 2z), evaluate the path integrals along the line of a to b: \vec{a}=(0,0,0), \vec{b}=(1,1,1), \int^{b}_{a} \vec{F} \times d\vec{r} \int^{b}_{a} \vec{F} ds Homework Equations No idea. The Attempt at a Solution I don't have a clue what these...
  42. I

    Help with cross product proofs

    I have a 23 problem assignment due at the end of the week, and although I'm going to have a chance to talk to my teacher about the questions I have, I'd like to go ahead and get going on the problems. I've successfully completed 21 of them, but the last two are stumping me. I'm submitting them...
  43. J

    Distributive property of the cross product

    Prove the following? Vectors (v-w)x(v+w)=2(vxw)
  44. R

    How Does Distributive Property Apply in Vector Cross Products?

    I was reading my physics book, and I stumbled across this : A_{x} \hat{i} \times B_{y} \hat{j} = (A_{x}B_{y})\hat{ i} \times \hat{ j}. I am trying to figure out, how can they use the distribute property ( I presume) like that? How did they factor the Ax and Bx out? I would have assumed it would...
  45. P

    Redundant cross product removed from Maxwell equation?

    I'm trying to track down the rationale for removing the cross product of velocity and magnetic field intensity from Maxwell's equation which specifies the value of the electric field intensity. In the third edition of "A Treatise on Electricity and Magnetism" Maxwell specifies (in modern...
  46. S

    Cross term gives the autocorrelation?

    I am reading a research paper about "narrow" autocorrelation and at the beginning there is an expression I don't unterstand http://www.wellesley.edu/Physics/brown/pubs/acv85_P1595-P1601.pdf" Does someone know what is meant with the word cross term?
  47. M

    Neutron absorption cross section

    Does anyone know anywhere where I can find reliable up-to-date cross section infromation? In particular I'm looking for the absorption cross section of Gadolinium-157 for thermal neutrons. Everywhere I look seems to give a different value ranging fro 70000barns up to 450000barns.
  48. B

    Cross Product of Vectors a & b: Why 0?

    I have not yet taken Linear Algebra, so perhaps that is why I don't have an answer to this question. But: Given a vector a <1,-1,0> and a vector b <-1,1,0>, I would suspect (by the right hand rule) that taking a X b, I would get a vector pointing out of the computer screen (assuming that...
  49. F

    Can a Cross Product Determine a Gradient Vector for a Non-Function Surface?

    This is a general question. If we have a parametric equation r(u,v) and we take r_u and r_v, then take their cross product, does it give us the gradient vector? Or just a vector parallel to the gradient vector?
  50. N

    Cross product in matrix determinant form

    Everything I have read indicates that the cross product is simply defined as a x b = i( ay*bz - az*by) - j( ax*bz - az*bx ) + k( ax*by - ay*bx ) and that it just so happens that there is a shorthand notation of cross product in matrix determinant form. How is the cross product...
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