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. Q

    Cross section computation - Huang's Statistical Mechanics

    I am reading chapter three of Huang's Statistical Mechanics and I have a problem with equation (3.22). Having discussed the derivation of the classical cross section for a scattering process, Huang moves on to the quantum version of it. He states that in quantum mechanics the fundamental...
  2. S

    Solving a linear equation with a cross product

    Homework Statement Suppose v is a vector satisfying: \alpha v + ( a \times v ) = b For \alpha a scalar and a, b fixed vectors. Use dot and cross product operations to solve the above for v. Homework Equations The unique solutions should be: v=\frac{\alpha^{2}b- \alpha (b \times a) + (b...
  3. F

    Second Moment of Area Problem for Floor Plate with Cross Beams

    Homework Statement So I need to know how to attack a problem for a solid metal plate. The plate is used as a manhole cover, so it needs to withstand a certain load. The load is calculated by placing a large weight at the centre of area 25x25. I can't for the life of me figure out how to do...
  4. C

    Estimating the order of magnitude of a ratio of two cross sections

    The question is "Make a simple estimate of the order of magnitude of the ratio of the cross sections (electron,positron->2photons) and (electron,positron->3photons)" Now I know that cross section is proportional to (1/q^4)*(Phase space factor)*(Coupling constant) where q^2 = E^2 - p^2. We are...
  5. S

    Are the Red Terms Equal to Zero in This Cross Product Problem?

    Background: we're trying to show that the rate of change of angular momentum of an object about its center of mass (position given by R) is equal to the total torque about R. Why are the terms in red equal to 0? If anything, shouldn't the terms circled in in blue be equal to zero since the...
  6. Y

    What is the cross section area of the water?

    what is the cross section area of the water?? Homework Statement Determine an expression for the cross sectional area A of the fluid in the tank as a function of D and H. Homework Equations A=pi*r2 The Attempt at a Solution i try to let the radius equal to the height but then the...
  7. M

    Cross product in spherical coordinates.

    Homework Statement i am trying to solve for the magnetic torque a circular loop of radius R exerts on a square loop of side length b a distance r away. The circular loop has a normal vector towards the positive z axis, the square loop has a normal towards the +y axis. The current is I in both...
  8. P

    Finding neutrino mean free path using cross section for interaction

    Homework Statement A supernova can produce a neutron star with typical radius 10km. Assume the neutron star matter consists of iron nuclei (A=56), produced by the electron capture reaction: e^{-}+Co\rightarrowFe+\nu_{e} The matter density is \rho=10^{5} tonne mm^{-3} and the neutrino...
  9. W

    Find Shear Centre of Cross Sections

    Please Help. Trying my best Homework Statement Locate the Shear Center of the Cross Sections Below: 1. http://tinypic.com/r/98xfd3/5 2. http://tinypic.com/r/15s4hfk/5 Homework Equations τ=VQ/IT The Attempt at a Solution 1. Moment = O Solve for Ve τ=VQ/IT...
  10. F

    Tabulated absorption cross sections.

    Yo does anyone have a table from like Brookhaven or somewhere of absorption cross sections for just about anything in the 1/v region? And have the precision included in the data. I'm doing a pretty quick statistics assignment.
  11. C

    Identity for the cross of a curl?

    Hello! I'm want to prove a vector identity for (\nabla \times \vec{A}) \times \vec A using the familiar method of levi-civita symbols and the identity \epsilon_{kij}\epsilon{kmn} = \delta_{im}\delta_{jn} - \delta_{in}\delta{jm}, but I don't seem to come up with any usefull answer. I...
  12. R

    A Moveable Cross wire and a Function of Time

    Homework Statement A circuit with a moveable cross wire is indicated in attached figure. The resistance is 2.5 Ω, the battery voltage is 5 V, the moveable wire length is 12 cm, and there is a uniform, constant magnetic field into the plane of the circuit (the page) with magnitude 0.3 T. (a)...
  13. T

    Understanding air particle velocity as cross product freq x disp

    I'm reading a book on microphones and came across the following: and then it goes off talking about something else... I feel stupid for asking this, but I don't get how the above equation works? For one, I thought cross products could only be be involving vectors? Aren't all the terms...
  14. S

    How do I calculate the cross section for a p p -> Z -> μμ process?

    Hi all. This is my first time in the Physics Forums. I would like to ask for guidance in a calculation of a cross section of a process. I know the Feynman graph but I'm completely lost on how to start the calculation.. For example.. p p -> Z -> μμ Many thanks in advance..
  15. M

    Electromagnetism - Cross Product of length and Magnetic Field

    Homework Statement A stiff wire 42.0cm long is bent at a right angle in the middle. One section lies along the z axis and the other is along the line y=2x in the xy plane. A current of 15.0 A flows in the wire-down the z axis and out the line in the xy plane. The wire passes through a uniform...
  16. J

    Unit vector cross products in different co-ords

    hey, i've been trying to work out how to determine the sign of cross products of unit vectors, for example in cylindrical, r x z = - theta theta x z = r r x theta = z i can't figure out the sign, r x z = |r||z|sinβ theta where β is the angle between them, which is 90°...
  17. G

    Schools Taking cross disciplinary subjects during Math graduate school

    Hello. While I am not heading off to graduate school for a little bit, I am interested in persuing a phd in pure mathematics (Geometry is a broad interest of mine). I would also be interested in taking one or two mathematically inclined graduate courses from the Physics department (String...
  18. F

    Confirmation for Simplifying Vector Product: Can Constants be Taken Out?

    this is a general question - the thing I'm working on if what i am asking makes sense - i am currently only looking for a confirmation on what i think is right this is a vector product question: if i have: (A/c x cB) can i look at that as: (1/c*c)(A x B) which comes to A x B the...
  19. Τ

    What is the Area of the Parallelogram?

    Homework Statement Let A = (-5, -2, -5), B = (-7, -7, -6), C = (-3, -3, 0), and D = (-5, -8, -1). Find the area of the parallelogram determined by these four points. Homework Equations Area of Parallelogram = ||a x b|| The Attempt at a Solution I drew the parallelogram and decided to use CA...
  20. A

    Typical cross sections for ee-uu scattering

    I'm numerically evaluating the differential cross sections \frac{\operatorname{d}\sigma}{\operatorname{d} \Omega} for e^{-}e^{+}\rightarrow\mu^{-}\mu^{+} scattering by integrating over \operatorname{d}\Omega = \operatorname{d}(\cos{\vartheta})\operatorname{d} \phi. Assuming no transverse...
  21. H

    Is there a vector that satisfies the property of the number 1 for cross product?

    Homework Statement Show that there is no vector ⃗e that has the property of the number 1 for cross product, namely that ⃗e × ⃗x = ⃗x for all ⃗x. Homework Equations I'm sort of stuck on how to show this. The Attempt at a Solution I set e=(e1,e2,e3) and x=(x1,x2,x3) and used cross...
  22. T

    3D Vectors Problem - Find Cross Product

    Homework Statement Given |\vec{a}| = 8, |\vec{b}| = 9 and the angle between vector \vec{a} and \vec{b} is 48° find the cross product, \vec{a} X \vec{b}. Homework Equations Let θ = angle between \vec{a} and \vec{b}. \vec{a} . \vec{b} = ( \vec{x}1 * \vec{x}2 ) + ( \vec{y}1 * \vec{y}2 ) + (...
  23. S

    You have a fine wire with a cross sectional area of 9.4×10−10 m2

    You have a fine wire with a cross sectional area of 9.4×10−10 m2 and a length of 1.1 m. You wish to determine what it is made out of, so you connect it to a standard AA battery (1.5 V) and measure a current of 0.048 A. What material is the wire most likely made out of? The options for the...
  24. A

    Cross Product application problem

    Calculating magnitude and direction of an magnetic force on an electron Homework Statement Okay so the question says that the magnetic force (Vector)FM on a particle which is in a magnetic field is found by (Vector)FM = Vector I x Vector B. Vector I = charge multiplied by the velocity of...
  25. B

    Hadron Cross Section Calculation

    Hi all, I'm trying to understand the solution to a problem from a textbook. We're asked to find the proportionality constant for $$\frac{d\sigma_{\rm elastic}}{dq^2}\propto e^{bt},$$ where q is the momentum transfer in a scattering process, defined in elastic scattering as...
  26. S

    Neutron Absortion cross section for an element

    I recently saw the Evaluated Nuclear Data File provided by Brookhaven national lab., where in i saw the plot of "Neutron Energy Vs cross section (total)" for different elements. http://www.nndc.bnl.gov/sigma/index.jsp?as=1&lib=endfb7.0&nsub=10 Now what i am interested in is, can we derive or...
  27. M

    How is the Cross Product Between Two Vectors Determined?

    The cross product between two vectors \vec{A}x\vec{B} and \vec{C} is given by the following equation: (\vec{A}x\vec{B})x\vec{C}=(\vec{A}.\vec{C})\vec{B}-(\vec{B}.\vec{C})\vec{A} Well, as I'm sure you know, proving something is true is different than proving how something is true. In this proof...
  28. B

    Application of the cross product: max height of z?

    Homework Statement http://www.scribd.com/doc/82645310 In Figure 3-31, the lines AB and CD are the center lines of two conduits 1 ft. and 2 ft. in diameter respectively. Determine the maximum value of z so that the two may pass without interference. Conduit CD must pass under AB...
  29. L

    Torsion on materials of variable cross section

    New here, sorry if I'm in the wrong place or unclear, etc. I've been looking at torsion on solid plates and the torsion constant. I was wondering how to handle the torsion constant on a plate of changing cross section (e.g. there are holes drilled in it, changing the area of the cross section...
  30. B

    Application of the cross product: max height of z?

    Homework Statement http://www.scribd.com/doc/82645310 In Figure 3-31, the lines AB and CD are the center lines of two conduits 1 ft. and 2 ft. in diameter respectively. Determine the maximum value of z so that the two may pass without interference. Conduit CD must pass under AB. Homework...
  31. M

    Cross product as a gradient?

    Is it possible to nontrivially represent the cross product of a vector field \vec{f}(x,y,z) with its conjugate as the gradient of some scalar field \phi(x,y,z)? In other words, can the PDE \vec{\nabla}\phi(x,y,z) = \vec{f}(x,y,z)\times\vec{f}^\ast(x,y,z) be nontrivially (no constant...
  32. N

    Capture Cross Section for a Neutron

    Homework Statement DT fusion produces 14.1 MeV neutrons. A diagnostic for a total fusion yield is the Cu-63( n, 2n)Cu-62 reaction. A) what is the threshold for this reaction? Cu-63 also undergoes a radiative capture reaction yielding Cu-64. This reaction has a thermal cross section of 4.5b...
  33. 2

    Clear up some cross product confusion for me

    Here is what I have A=xro+yr1 B=yro+xr1 I need to find A x B I am confused about do it because The components of A and B are in terms of vectors If A = 3i + 4j + 7k and B = 2i + 2j + 1k I would have no problem (these numbers are meaningless just giving an example) finding A...
  34. S

    What is Born cross section?

    Hi everyone? What is Born cross section? And what is the relation between it and observed cross section? Thank you.
  35. C

    Hydrogen Cross Section Resonances

    Homework Statement Why don't hydrogen cross-sections exhibit resonances? Homework Equations N/A The Attempt at a Solution I was thinking it had something to do with the spin, the fact that is has only one electron, or elastic scattering, but I can't seem to wrap my brain around...
  36. O

    Cross section of coulomb sacttering vs Rutherford

    differential cross section of coulomb scattering can be expressed as a form factor times Rutherford one, we model the charge we used spherically symmetric charge density, if we replace this point charge with other distribution like Gaussian , what is the difference between these two models, is...
  37. P

    Understanding Dot and Cross Product in Matrix Multiplication

    Explain, for example, why you can cross three vectors (two at a time, following the usual rules), but not dot three vectors. Do you see the dot product "in action" in matrix multiplication? What sort of insights can the dot product give when trying to comprehend matrix multiplication?
  38. F

    Rotation around the z-axis and cross products

    Homework Statement A defining property of a vector is that its components must transform in a particular fashio under a rotation. for a counterclockwise rotation around the z-axis, by and angle ∅ the components Ax, Ay, and Az of a vector A transform in the following fashion: Ax --> Ax' =...
  39. L

    Dot and Cross Products: Solving for [u x v] - 0, Simplification and Distribution

    Homework Statement u (dot) [ u x v] Homework Equations The Attempt at a Solution The answer is 0, but I'm not sure why. Do you simplify [u x v], then use that vector to dot it with u? Or can you distribute the u to both u and v?
  40. tom.stoer

    Energy-dependent cross ection and mean free path

    The mean free path is usually determined via the scattering cross section σ; one starts with a differential equation for the intensity dI(x)= -n\,\sigma\,I(x)\,dx Are there generalizations for this derivation for energy-dependent cross sections σ(E)?
  41. D

    Heating a 7 cm long copper wire of cross sectional diameter .75mm

    hi guys, m a lil stuck here what voltage would be rquired to heat a 7cm long copper wire of .75mm diameter in about 2-3 seconds.the target temp is 400-450c. dr ankit
  42. G

    What are the Cross Products of Vectors AB and AD in Calculus 3?

    Homework Statement see attachment Homework Equations The Attempt at a Solution i found AB got <4,2,3> i found AD got <1,-1,1> i found |ABxAD| got square root of 62 not exactly sure what i am doing wrong thanks for any help
  43. J

    Calculate the size of the cross section relating to tension

    Homework Statement A medium carbon annealed steel rod has a rectangular cross section and must cope with a tension of 3 tonnes. The thickness of the rod is 15mm. Calculate the size of the cross section. Tension limit = 3 tonnes Thickness = 15mm Cross Section = ? Homework Equations...
  44. E

    Determining Delay with Cross Correlation

    Homework Statement Let x(t) be a transmitted radar pulse. The received radar pulse is y(t). y(t)=ax(t-t_{d})+v(t) Where v(t) is the additive noise and td is the time delay. The signals x(t) and y(t) are sampled and processed digitally to determine the delay The discrete time signals...
  45. S

    Question on the History of the Cross Product

    I am trying to get an intuition behind the cross product but i seem to get stuck with understanding why we make the vector perpendicular to the other two? I understand the need to define an orientation for physical systems like torque (ccw or cw) but then why make it a vector and why choose...
  46. 4

    Magnitude of Cross Product Mismatch

    Homework Statement Find the magnitude of the vector product w ⃗x u, where w=<1,0,1> and u=<1,1,0>. Homework Equations ||w x u|| = ||w|| ||u|| sin θ cos θ = \frac{w.u}{||w|| ||u||} The Attempt at a Solution w ⃗x u ⃗= -i ̂+j ̂+k ̂ ‖||w ⃗x u|| ⃗ ‖= √3 but...
  47. lonewolf219

    Calculus 3 introduction to cross product

    Just learning about vectors in 3 dimensions. Would it be correct to think of the cross product vector like a resultant vector? Is it similar to the displacement? If so, why is it always 90 degrees from both original vectors? If anyone has some deeper insight into any of these vector topics...
  48. A

    Verify the Product Rule for cross products

    cross products= vector(a)*vector(b)=Magnitude(a)*magnitude(b)*cos(theta) I'm having trouble on how to get started...
  49. R

    Cross section of a stream flowing from a hole

    Homework Statement Consider a cylindrical tank filled with water with 2.5-m depth. The water emerges from a small hole at the center of the bottom, as shown in the figure. The diameter of the hole is 1 mm. The cross-section area of the vertical water stream decreases as it falls. Find the...
  50. E

    Advanced Vecor calculus - Cross Product

    Homework Statement For arbitrary vector fields A and B show that; ∇ ^ (A^B) = (∇ . B)A - (∇.A)B + (B.∇)A - (A.∇)B Homework Equations where (A.∇)B = ((A.∇)Bx, (A.∇)By, (A.∇)Bz) and (A.∇)f = Ax δf/δx + Ay δf/δy + Az δf/δz = (Ax, Ay, Az)( δf/δx, δf/δy, δf/δz)f The Attempt at a...
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