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. R

    Classical Book on Cross and Dot products

    I had a book on dot and cross products, and the author presented his material in terms of Maxwell's equations. It's a popular book. Alas, I can't remember the title or author. I was going to loan it to a friend but found the book missing. The book isn't long at all and is a paperback book...
  2. A

    Why is A cross B= ABsin(theta) false?

    Homework Statement problem 2.2(b) Homework Equations A cross B = ABsin(theta) The Attempt at a Solution I believe that the answer is that you cannot multiply two vectors but you can dot or cross them. In order to make this a true statement you have to take the magnitudes of A and B.
  3. Muthumanimaran

    Vector Cross Product Homework: Expand $\vec{v}\times({\nabla}{\times}\vec{A})$

    Homework Statement This is not a homework problem, I am currently reading the Derivation of potential of a charged particle in Electric and Magnetic field from the book Mechanics by Symon (I attached the image of the page), I need to know how to expand the vector cross product such as...
  4. A

    I need to prove del cross f= 0

    Homework Statement F(x) has the form F(x)=f(r)x where r=|x| A.) prove that del cross f =0 B.) Now suppose also Del •F = O. What is the most general form allowed for f(r)? Homework EquationsThe Attempt at a Solution I have done part b but what do I need for A F(X)= r(hat) Fr = 1, F(theta)...
  5. J

    Cross Product Help - Find Magnitude of Last Two Products

    The first part of the problem was easy enough as was finding the directions of the other two, but I am having trouble finding the correct angle for the last two cross products in order to find the magnitude.
  6. steele1

    Prove area of triangle is given by cross products of the vertex vectors....

    Homework Statement The three vectors A, B, and C point from the origin O to the three corners of a triangle. Show that the area of the triangle is given by 1/2|(BxC)+(CxA)+(AxB)|. Homework EquationsThe Attempt at a Solution I know that the magnitude of the cross product of any two vectors...
  7. F

    How do I cross Del with (scalar*vector)?

    Homework Statement Show that for any scalar field α and vector field B: ∇ x (αB) = ∇α x B + α∇ x BHomework Equations (∇ x B)i = εijk vk,j (∇α)i = αi (u x v)i = eijkujvk The Attempt at a Solution Since α is a scalar i wasn't quite sure how to cross it with ∇ So on the left side I have...
  8. S

    Cross Product Properties Question

    Homework Statement A\cdot B\times C\quad =\quad 2\\ (2A+B)\quad \cdot \quad [(A-C)\quad \times \quad (2B+C)]\quad =\quad ? Homework Equations Various cross product and dot product properties The Attempt at a Solution I've only managed to get so far, don't really know what to do next A\cdot...
  9. Y

    Mechanics of Materials: Cross Sectional Area Problem

    https://www.physicsforums.com/threads/mechanics-of-materials-homework.855915/']<Moderator's[/PLAIN] note: thread moved from a technical forum, so homework template missing.> https://www.physicsforums.com/threads/mechanics-of-materials-homework.855915/ This is a link to a problem which I am...
  10. Mr Davis 97

    B Deriving law of sines from cross product

    I am trying to derive the law of signs from the cross product. First, we have three vectors ##\vec{A} ~\vec{B} ~\vec{C}## such that ##\vec{A} + \vec{B} + \vec{C} = 0##. This creates a triangle. Then, we label the angles opposite the respective sides as a, b, and c. I am not sure where to go...
  11. Jackie CH Liu

    A A Quantum Theory of Spacetime, the Physical Reality of Cross

    I just want to share my paper I recently wrote. I am trying to submit for publication: [Reference to unpublished paper deleted]
  12. kontejnjer

    Moller scattering polarized cross section

    Homework Statement [/B] (Note: this is not strictly homework, but it is related to one course I'm doing, and I can't find a useful solution anywhere) Find the analytical expression for the scattering cross section of two longitudinally polarized electrons at tree level. Homework Equations...
  13. zihao yu

    A Discover the Cross Section of η′→γγ and Its Calculation Methods

    Is there any measure for cross section of η′→γγ? Or has anyone did the calculation??
  14. M

    Calculating Cross Section

    Homework Statement I have a problem in calculating cross-section in elektron-positron -> muon-antimuon scattering. Homework Equations In the relativistic limit, we find the differential cross-section of {e}+{e^-} -> {μ}+{μ^-} is \frac{d\sigma}{d\Omega}=\frac{\alpha^2}{4s}*(1+cos^2{\theta})...
  15. parshyaa

    I Vector Cross Product: Understanding the Perpendicular Result

    Why mathematicians defined that the cross product of vector A and B will be a vector perpendicular to them.
  16. Safinaz

    I How to estimate this cross section

    Hi all, Do any has an idea how to give a rough estimation for this process's cross section: g g -> H -> h h, (h -> b b~), ( h -> b b~) ? where h is SM Higgs and H is a heavy Higgs boson with BR (H > hh) ~ Gamma (H > hh) ~ 10^-3 GeV and sigma (g g > H ) ~ 10 pb .. When I calculated it by...
  17. Safinaz

    I How to know the cross section in this Figure

    Hi all, Do anyone familiar with these analysis of cross section ? I wonder how to find the cross section of ( p p ## \to \gamma \gamma## b b~) (blue region) in the opposite plot, the y-axis is the number of events divided by 100 GeV with luminosity = 100 ##\mbox{fb}^{−1 }##.. The Fig. from...
  18. S

    Cross section change and failure of tube

    Hey, working on something for a personal project and was wondering if you could point me in the right direction. I have a 47 inch hollow steel tube that I'm going to cut the end 6 inches into a half circle tube . I have a load of 200 lb at the top and am wondering how about I would quickly...
  19. H

    Vector cross product with curl

    Homework Statement Using index-comma notation only, show: \begin{equation*} \underline{\bf{v}} \times \text{curl } \underline{\bf{v}}= \frac{1}{2} \text{ grad}(\underline{\bf{v}} \cdot \underline{\bf{v}}) - (\text{grad } \underline{\bf{v}}) \underline{\bf{v}} \end{equation*} Homework Equations...
  20. W

    Hardy Cross method correction problem

    Homework Statement I have problem with the flow rate (Q) in junction that join 2 loops together , where k = 4 , Why in the second correction , the corrected Q in first and second loop = 21 clcockwise for left loop , and for 21 anticlockiwise for right loop ? Homework EquationsThe Attempt at a...
  21. F

    What value should be used for junction CA in the Hardy Cross method?

    Homework Statement i have a netwrok of pipe as shown in the figure . I'm asked to find the flow rate using HARDY CROSS method . in the second trial of first loop at junction CA , which value should i use ? -15.3 from the corrected in second loop ? or 22.7 from the corrected value in the first...
  22. F

    Using corrcted value for Hardy Cross method?

    Homework Statement i have several example of hardy cross problem involve 2 loops , for the junction that divide 2 loops , is it necessary to use the corrected value for the junction on second loop for the first trial ? or just use the initial assumption will do ...
  23. F

    Solving the Hardy Cross Problem

    Homework Statement in this problem , we know that Q (flow rate ) has power of 2 , hf = k(Q^2) , shouldn't the hf = k(Q^2) has positive value ? Homework EquationsThe Attempt at a Solution since (554)(-40^2) will become positive , same thing goes to hf / Q , when the hf = positive , the hf / Q...
  24. prashant singh

    I Is There Proof for the Cross Product Matrix Formula?

    Is there any proof for the matrixx formula of the cross product. I am asking this because I have seen many videos and they have used the matrixx formula and then proved that ||A X B|| = ||A|||B||sin(theta), khan academy also used the same method
  25. O

    Understanding cross product and direction of torque

    Homework Statement Hi everyone, I am a first year physics student and we recently learned about torque. Every time I think I understand it something else comes up to confuse me - this time it is the direction. I tried looking in the forum and generally in google, but everyone only explains the...
  26. prashant singh

    I Cross product or vector product.

    What does the angle theta acutally means in cross product because I have seen in many places it is written that theta is the angle at which two vector on a given plane will coinside with each other so that there will be only one direction. Is it true and why they defined it in this way , I...
  27. arpon

    I Physical significance of integral of F cross dr

    In the vector calculus course, I calculated integrals like, ##\int \vec F \times \vec{dr} ## Does this kind of integrals have physical significance or practical application other than Biot-Savart's Law?
  28. B

    Exploring Cross and Auto-Correlation in Time and Frequency Domains

    Homework Statement 1. Given two vectors x = [0 0 1 0 0 ] and y = [0 0 0 0 1] find the cross correlation and the time difference between the pulses if the sampling frequency is 1kHz? 2. Given this vector calculate the auto correlation and if the signals is sampled at a frequency of 1MHz...
  29. Rheegeaux

    Moment of inertia of a cross system

    Homework Statement Two identical rods, each with mass 5.00 kg and length 2.00m are welded as shown in the figure. If the moment of inertia of a rod about an axis passing through its center is Icm = 1/12ML2, what is the moment of inertia of the system of rods about an axis perpendicular to the...
  30. P

    Difference of B-10(n,2a)H-3 cross section in ENDF/B

    In the research,it is found there is significant difference of B-10(n,2a)H-3 reaction cross section between ENDF/B-V and ENDF/B-VI (http://www.nndc.bnl.gov/).The cross section in ENDF/B-V is 10 times less than ENDF/B-VI when neutron energy...
  31. ChrisVer

    A Why do NLO cross sections sometimes decrease relative to LO ones?

    I was wondering, can the calculation of the NLO cross section decrease the cross section (relative to the LO one)? or not? I am asking because I read here http://www.pa.msu.edu/~huston/Kfactor/Kfactor.pdf the following Which refers to Table 1 and cases where the K-factor appears to be less...
  32. M

    How can I move my bed and mattress from Oregon to New York on a budget?

    Hi PF! I am moving from Oregon to New York for grad school and am wondering the cheapest way to move my bed and mattress. Any ideas? I don't think the best route is to buy a new bed and mattress in NY. Thanks!
  33. G

    Hybrid vs Crossbreed: What's the Difference?

    What is the difference between a hybrid and a crossbreed?
  34. ChrisVer

    A Cross sections of bins and combination

    suppose you have 2 bins each with cross section \sigma_1, \sigma_2... if you combine those bins, is it a logical assumption to say that the cross section will also be added? I suppose from the equality of the luminosity one can get: \frac{1}{2}[ N_1 / \sigma_1 + N_2 /\sigma_2] = N_{1+2}/...
  35. G

    A Pp total cross section and asymtotic freedom

    Hi! On page 12 of http://pdg.lbl.gov/2009/reviews/rpp2009-rev-cross-section-plots.pdf one can see the total cross section increasing beyond a certain treshold. At higher energy protons (and their quarks) have a shorter wave length and so they can become closer an closer and the strong force...
  36. J

    I What is the resolution to the problem with E cross B field and E>B?

    I have been unable to find a satisfactory explanation of this problem, elsewhere. Consider an uniform electric field, E, along the y axis. Consider also a uniform magnetic field, B, along the z axis. If we release a particle (charge=q, mass=m) at rest on the origin at time t=0, what will be...
  37. H

    Cross Product: Right-Hand Rule Explained

    In the cross product, why is vectorA*B=-(vectorB*A) How does the right-hand rule apply to this formula?
  38. Spinnor

    Cross between helicoid, complex plane wave

    Function kind of cross between a helicoid and a complex plane wave? I would like to translate a mental picture into a mathematical expression if possible. The picture might be roughly thought of as a cross between a complex plane wave and a helicoid. A construction I think goes as follows, take...
  39. W

    Berry's Curvature Equation cross product calculation

    Hi, The following textbook Heisenberg's Quantum Mechanics shows an example of calculating Berry's curvature (top page on pg 518). It led to a following equation Vm= (- 1/B2 ) * i *∑ ( <m,B|S|n,B> ∧ <n,B|S|m,B> ) / A2 ...[1] the textbook claims that we add the term m = n since <m|S|m> ∧ <m|S|m>...
  40. Dave Ritche

    Cross browser website question

    I have designed a webpage and i opened it in chrome.It worked quite fine and all the layouts were at their position but when the same page i opened in internet Explorer messed up and the layouts weren't at their position.In firefox,only the header section showed up.What is the problem?Howcaan it...
  41. T

    Calculate terminal velocity when given cross sectional area

    Homework Statement Two packages are dropped from an airplane. A parachute can increase the cross sectional area of each packages by a factor of 31. The parachute on package 1 fails to open, and the terminal speed of package 1 is 10 m/s. The parachute on package 2 opens. What is the terminal...
  42. Z

    Understanding the Relationship between Dot and Cross Products

    Homework Statement Find (u• v) 2 + ||u × v||2 , given ||u|| = 5 and ||v|| = 3 Homework Equations u•v=||u|| ||v|| cos(x) u×v=||u|| ||v|| sin(x) The Attempt at a Solution Using these two equations I squared them both, brought them together and ended up with 225cos2(x) + 225sin2(x) and received...
  43. Safinaz

    Higgs production cross section

    Hi all, I try to find the exact calculated gluon- gluon fusion cross section for the SM- Higgs with mass 125 GeV, for instance at CME = 14 TeV. I found on twiki page: " https://twiki.cern.ch/twiki/bin/view/LHCPhysics/CERNYellowReportPageAt1314TeV#s_14_0_TeV " ##\sigma(gg \to h) = 49.47~ pb##...
  44. S

    Peskin and Schroeder - page 4 - spin and cross section

    In chapter 1 of Peskin and Schroeder, the reaction ##e^{+}e^{-}\rightarrow \mu^{+}\mu^{-}## is studied in detail. The related following paragraph is taken from page 4 of Peskin and Schroeder: Both the electron and the muon have spin ##1/2##, so their spin orientations must be specified. It is...
  45. ORF

    What causes a plateau in the cross section of neutrons?

    Hello It seems to me that the nuclei have a flat elastic scattering cross section of neutrons, for neutron energies from eV to MeV. http://www.nuclear-power.net/wp-content/uploads/2015/11/Elastic-Scattering-Cross-section-light-elements-min.png I thought that maybe it was caused because the...
  46. DuckAmuck

    Can a cross product be defined between two Hilbert space vectors?

    The equivalent of a dot product in Hilbert space is: \langle f | g \rangle = \int f(x) g(x) dx And you can find the angle between functions/vectors f and g via: \theta = arccos\left( \frac{\langle f | g \rangle}{\sqrt{\langle f|f \rangle \langle g|g \rangle}} \right) So is it possible to...
  47. ognik

    MHB Please check Cross product solutions

    I'm not 100% confident of my approach to the 2 exercises below: Orbital angular momentum of i'th element is $\vec{L_i} = \vec{r_i} \times \vec{p_i} = m_i \vec{r_i} \times (\omega \times \vec{r_i}) $ a) Find the inertia matrix $I$ such that (omitting vector signs from here on) $L = I \omega, |L...
  48. K

    Column analogy (Hardy Cross) - Carry Over Factor and stiffness

    Hi all, 1. Homework Statement Book example: Determine using the column analogy method, the carry over factor from A to B and the stiffness at A for a propped cantilever. (Propped end is defined as A, and fixed end is defined as B) 2. Relevant principles 1. Moment at any point M = M_{s} -...
  49. Odious Suspect

    Geometric proof cross product distributes over addition

    If the cross product in ℝ3 is defined as the area of the parallelogram determined by the constituent vectors joined at the tail, how does one go about proving this product to distribute over vector addition? I've attached a drawing showing cyan x yellow, cyan x magenta, and cyan x (magenta +...
  50. S

    Relation between cross section, scattering angle and KE?

    I'm trying to figure our the relation between cross section, scattering angle and KE? I'm doing a few exercises where I've been given kientic energy and scattering angle and have to calculate the cross section. Cross section is in units of Barns (m2), and KE is 1/2 kg*m2*s-2, but I can't seem...
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