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. G

    What time t does the particle first cross the x axis?

    1. (a) A particle has ~r(0) = (4 m)j and ~v(0) = (2 m/s)i. If its acceleration is constant and given by ~a = −(2 m/s2) (i+j), at what time t does the particle first cross the x axis? Answer in units of s. (b) At what time t is the particle moving parallel to the y axis; that is, in the...
  2. T

    Aligning 3 point plate - vector cross product useful?

    Homework Statement Hello, I have a plate that needs levelling. I can only twist the back 2 feet threaded feet, while the single front foot is fixed, as in the diagram: As mentioned above I can only TWIST the back two feet (separately or together) causing the plate to tilt around the...
  3. M

    How Do I Correctly Calculate the Torque in This Physics Problem?

    Homework Statement the question is sample problem 11-3 of 'fundamentals of physics' 7th edition. Three forces, each of magnitude 2.0N, act on a particle. the particle is in the xz plane at point A given bz position vector r, where r0 3.0M and theta=30°. Force f1 is parallel to the x...
  4. K

    Vectors ; specifically cross product application

    Homework Statement vector A = 1.5i + 6.7j - 7.4k vector B= -8.2i + 6.5j + 2.3k (f) What is the magnitude of the component of vector A perpendicular to the direction of vector B but in the plane of vector A and B. The Attempt at a Solution This part of the problem has me kinda...
  5. S

    Proof for cross product a x b= -b x a

    This problem involves vectors and it's a fairly basic proof but I can't seem to wrap my head around it. I tried to just separate the vectors into their components and cross them but then I just get another set of coordinates that doesn't seem factorable. I really can't see any way to...
  6. F

    Understanding Vector Multiplication: Why Does Cross Product Result in a Vector?

    Homework Statement This is actually a concept question, but since its kind of elementary i post it here I understand the calculation of the cross product, what i do not understand is why the cross product that only involve in 2 dimension will have the result of 3rd dimension Homework...
  7. E

    Proving Cross Product distributivity, but

    ... with the cross product being only defined as: A X B = |A| |B| sin \theta times a unit vector perpendicular to the plane of A&B (direction according to the right hand rule, in the usual way). where theta is the smallest angle between vectors A & B. A X ( B + C ) = A X B + A X C is the...
  8. E

    Getting Extinction cross section from Radar cross section using HFSS

    Hi, Has anyone tried using the HFSS software to get the extinction cross section of a particle? I've been told that the extinction cross section of a particle is the imaginary part of the radar cross section in forward direction, so I did exactly what the RCS tutorial from HFSS did, except...
  9. matqkks

    Why is the Vector (Cross) Product pxq Perpendicular to a Plane?

    Given two vectors p and q, why is the vector (cross) product pxq perpendicular to the plane containing these vectors? Is there a geometric or physical way of explaining why? Are there any real life examples we can draw from?
  10. S

    Obtaining Temperature-Dependent MCNP Cross Sections Without NJOY

    hello, i am using mcnp for a reactor kinetic study.the only problem is, to establish the model i need to calculate the temperature coefficients, and in order to do that i need to calculate k in different temperatures and therefor need a mcnp library that contains cross-sections for a multitude...
  11. J

    Graphical Representation of Cross Product

    Homework Statement Show graphically how \vec{a}\times\vec{x}=\vec{d} defines a line. \vec{a} and \vec{d} are constants. \vec{x} is a point on the line.Homework Equations \vec{a}\times\vec{x}=a\cdot x\cdot sin(\theta)\cdot \hat{n}The Attempt at a Solution Not sure if the included relevant...
  12. S

    Why is the cross product defined as it is?

    We all know and love the determinant form of the cross product: \bold{a}\times\bold{b} = \left|\begin{array}{ccc} \bold{i} & \bold{j} & \bold{k} \\ a_x & a_y & a_z \\ b_x & b_y & b_z\end{array}\right| and can calculate this by going through the motions but when I try to think...
  13. Z

    Finding Cartesian Components Using Cross Product for Magnus Force Calculation

    The pure math of the problem: I have two vectors, both of which are expressed in spherical coordinates. I know the magnitudes as well as the polar and azimuthal angles that express these vectors. In addition, I have a third vector. I only know the magnitude of this vector, and I need to...
  14. S

    Cross product of complex vectors

    Would you pls help me with the following vector product? I got no idea how the author derived the second equation from the first one. My derivation result is always including the imaginary unit i for the second term in the second equation on the right hand side. Specifically, how to verify that...
  15. P

    Cross correlation in two data sets of the same sample population

    I have the following problem: Suppose there is a survey of persons with two properties each (a and b). a can take a relatively small number of values (say the political inclination: Conservative, Liberal, Socialist, or Other) the other one b can take a large number of values (say: the country...
  16. S

    Cross section data, how to fill in the gaps?

    I wanted information on the 18F production rates of 18O(p,n)18F compared to 20Ne(d,alpha)18F. I found a 1979 graph that showed some nice curves between 2.3 and 22 MeV but I wanted to see what things looked like between 1 MeV and 2.5 MeV. So I went here...
  17. I

    Hardy Cross Moment Distribution Problem

    Hi Guys, I have a 2nd year structural analysis problem which I am hoping someone can help me with. Homework Statement T-shaped, indeterminate frame consisting of two members connected at a node in the middle with the bottom member joined by a fixed pin-joint and the top member connected...
  18. A

    The prism is made from glass and its cross section is an

    Homework Statement the prism is made from glass, and its cross section is an equilateral triangle. the indices of refraction for the red and violet light are 1.662 and 1.698, respectively. the angle of incidence for both the red and violet light is 60 degrees. find the angles of refraction at...
  19. S

    Differential cross section formula of electron-positron pair production.

    Homework Statement I need to calculate the differential cross section in order of Mandelstam variable t, instead of the angle \theta. My problem is with the change of variable not the amplitude of the process. I'm getting a global minus sign which can only be wrong. It seems I'm making a very...
  20. Z

    How Does Chirality Affect Weak Decay Cross Sections?

    Weak decay -- cross sections I have to estimate the ratio between the cross sections of the following weak processes: \nu_{\mu} + e^{-} \Rightarrow \nu_{e} + \mu^{-} \bar{\nu_{e}} + e^{-} \Rightarrow \bar{\nu_{\mu}} + \mu^{-} My teacher says that as the first process is LL \Rightarrow LL...
  21. S

    Biology Understanding Genetics: Predicting Phenotypes in a Dihybrid Cross

    [b]1. Homework Statement In an organism, two separate genes influence the length of the hair. The allele for long hair, L, dominates the allele for short hair, l. The allele for hair, H, dominates the hairless allele, h. In the cross between parents of genotype LlHh and llHh, what ratio of...
  22. T

    Flux attenuation, given interaction cross section

    It strikes me that this may well be fairly easy, but i can't quite get my head round the correct way to lay this problem out (at least in a mathematical sense). If you are considering a neutron flux onto a fully understood material, and you also know the neutron interaction cross section of...
  23. S

    Understanding Del Operation on Vector U Without Dot or Cross Product

    hi, I'm trying to follow a derivation in a paper and this equation is confusing me: (u'.\nabla)U = (\nablaU).u' Where U and u' are velocities. The operation of del on the vector U without a dot or cross product is giving me some grief. Can someone explain how this works to me...
  24. P

    Two charged capacitors cross connected to each other

    Homework Statement Capacitors C1 = 6.99 mF and C2 = 1.72 mF are charged as a parallel combination across a 219 V battery. The capacitors are disconnected from the battery and from each other. They are then connected positive plate to negative plate and negative plate to positive plate...
  25. A

    ABAQUS 6.9 Meshed Beam Cross Section

    I need help with my beam structure in abaqus. The beams I need to model are hollow and elliptical. This is not included in abaqus' library or profiles. So I want to make a Meshed beam cross section as described in the manual. However, the manual is quite difficult to understand. Can someone...
  26. A

    Volumes of Cross Sections with Perpendicular Planes

    Hey guys I am new here i was wondering if anyone can help me understand this problem better Homework Statement The base of a certain solid is the circle x^2 + y^2 = 9. Cross sections of the solid with planes perpendicular to the y-axis are semicircles with their diameter in the base of the...
  27. M

    Cross sectional area (NOT A QUESTION)

    Just for those who don't know a thing about cross sectional areas, I thought I'd explain. A cross sectional area describes the area of a flat (2-dimensional) representation of a 3-dimensional object. So if I cut a cylinder, instead of seeing two circles, I see four circles (unless there are...
  28. M

    Compton Cross Section: Derivation & Relation

    What's the relation for the Compton cross section? I remember it going as 1/(1-cos(theta)) but can't remember the rest. I searched for a derivation but can't find one at the moment.
  29. R

    Cross Section of Water Flowing Down Vertical Pipe: The Mystery Unveiled

    hi We all know when velocity of fluid increases then cross section decreases for same mass flow rate and this can be well seen at water flowing from a height as in waterfalls. But why this doesn't happen when water flows down through a vertical held pipe of constant cross section. Well you may...
  30. E

    What is the connection between path integrals and cross sections?

    Hey folks, i am currently making myself familiar with the path integral in high energy physics by reading Lewis Ryder's QFT book. I do have a question however, since i do not really understand the connection between the path integral and the cross section of a process. Are they only related...
  31. E

    Calculating Radar Cross Section

    I am trying to write a program to numerically calculate RCS using geometrical optics (or some form of it). Basically my idea was to cast a bunch of rays from an emitting object (in my code it is a 1 m^2 plate), find where they intersect a surface, reflect the rays off of this surface and see if...
  32. Q_Goest

    Seeing Double: Superimposing a Real Cross Section onto a CAD Model

    This was pretty cool. I had to draw the cross section of a quad seal (on CAD). It’s basically an O-ring with a cross section that looks like a deformed square with these lobes on the corners. It looks like this: http://www.daemar.com/images/Quad-Ring-PartingLine.jpg But I don’t have...
  33. D

    Finding the shear centre of a non-homogeneous cross section cross

    for the following cross section the ratio Eb/Ep=30 find the shear centre of the cross section ------------------------------------------- first of all i need to find the equivalent cross section, which will be the same except that the horizontal parts will be of length n*L=30*1=30cm...
  34. L

    Understanding the Derivative of the Cross Product in Dynamics

    Homework Statement http://damtp.cam.ac.uk/user/dt281/dynamics/two.pdf" Looking at page 5, equations (2.19) and (2.20) The Attempt at a Solution I cannot understand how they derived the (2.20), at first from comparing the solutions I had assumed r(dot)' had disappeared as we were...
  35. M

    Cross product invariant under SO(3)-matrices?

    Hi there!I'm trying to prove the following obvious statement, but am somehow stuck :( Let \vec a,\ \vec b\in\mathbb{R^3} , let M be in SO(3) and x be the cross productprove: M(\vec a\times\vec b)=M\vec a\times M\vec bI tried using the epsilon tensor, as in physics, but it doesn't really...
  36. 1

    Mastering Cross and Dot Products for Test Review

    i'm reviewing for a test and I can't remember how to do the cross product of (2A)x(3B) or how to find the angle theta when given components. or dot product: 2A . 3B
  37. S

    Proving Parallel Vectors: Cross Product Question Explained

    Homework Statement Prove that If \vec{a}x \vec{b} = 0, then \vec{a}is parallel to \vec{b}. Homework Equations The Attempt at a Solution I tried attempting the solution by using the following: \vec{a} = [a1, a2, a3] \vec{b} = [b1, b2, b3]When I took the cross product of a x b I got...
  38. J

    Angular Velocity Calc: Cross-Shape Object, KE, MOI, Energy

    There is a cross shaped object with masses on each arm, the arms are different lengths and they are perpendicular to each other. the longer rod, (7m radius from center) has two 12kg masses, one on each end. The shorter rod (3.5m radius from center) has two 24kg masses one on each end...
  39. S

    Rutherford Scattering cross section

    Homework Statement Integrate the rutherford cross section over the backward hemisphere to get 4pi(sigma0(E)) Homework Equations Rutherford cross section is sigma0(E)/sin^4(theta/2) The Attempt at a Solution When I integrate this with the limits pi/2 to pi i get sigma0(E)*(8/3) i...
  40. 2

    Definition of the Cross Product?

    Hi Guys, I realize that this may seem like a really simple question but it's really driving me crazy. In my A-level maths we've just started looking at the cross product and I understand how to calculate it, it's application in calculating areas ect but I find myself not understanding what...
  41. G

    Cross Product - Determinant form

    Did someone just realize that taking the determinant of a specific matrix gives you the cross product formula, or is there is a specific conceptual reason why it works?
  42. I

    What does dσ/dΩ represent in terms of particle scattering?

    What is physically meant by: \frac{d \sigma}{d \Omega} Where \sigma is the cross section and \Omega is solid angle. I can't really picture it.
  43. P

    Neutron microscopic cross section data

    Hi guys, I am trying to calculate the macroscopic cross section (scattering and absorption) for high energy neutrons between 1 MeV and 10^7 MeV in Silicon. I am using the macroscopic cross section to determine the mean free path. To calculate the macroscopic cross section, i need to know the...
  44. S

    Origin of Vector Cross Product

    I understand the cross product of vectors to some degree and i can calculate. But i don't really understand the origin of the cross product What does a vector cross product mean in physical terms. Vector addition is quite easy to understand. I don't think the cross product is 'multiplication...
  45. A

    Cross product for parallel vectors

    Homework Statement Is the line through (4,1,-1) and (2,5,3) parallel to the line through (-3,2,0) and (5,1,4)? Homework Equations The Attempt at a Solution Line one 'direction' = (-2,4,4) = A Line two 'direction' = (8,-1,4) = B I remember that the cross product of two...
  46. W

    Dot product and cross product of vectors

    Homework Statement This isn't so much a problem of calculation, so much as it is I need to know if i did it right, you'll see what I mean. vectors v=(2,0,2), u=(-1,1,0), w=(0,-1,1) Computer the quantities that make sense (a period denotes the dot product, x denotes cross product)...
  47. F

    Volume of Solids with Known Cross Sections (Calculus AB)

    Can anyone help me with this calculus problem? I have tried it a couple of different ways, but keep getting various incorrect answers; I think my problem is probably in the setup. I am trying to find the volume of the solid created by revolving the area bounded by these two equations y = 6 -...
  48. J

    Transformation of cross product

    If A\in O(3) and v,w\in\mathbb{R}^3, then (Av)\times (Aw) = (\textrm{det}\;A) A(v\times w) is right, right? Is there any simple way of proving this? It doesn't come easily like invariance of dot product. Isn't this equation also important for understanding the pseudovectors?
  49. P

    Cross product by epsilon ijk method

    Homework Statement I need to calculate Ax(BxC) -A, B, C are vectors, apart from bac-cab rule, I need to get it by epsilon ijk -Following I will note it by e(ijk). Homework Equations I expect answerer to know kronecker delta equation and vector multiplications. The Attempt at a...
  50. Ƒ

    How Is the Magnitude of the Cross Product Related to Parallelogram Area?

    How do you prove that ||VxU|| is the area of the parallelegram they form? I know that the cross product is a vector perpendicular to V and U
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