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. chwala

    Obtain an equation of the plane in the form ##px+qy+rz=d##

    The solution is here; Now to my comments, From literature, the cross product of two vectors results into a vector in the same dimension. A pointer to me as i did not know the first step. With that in mind and using cross product, i have ##(1-1)i - (-1-1)j+(1+1)k =0i+2j +2k## as shown in ms...
  2. .Scott

    B Crossing the Bekenstein Bound at Black Hole Event Horizon

    The Bekenstein Bound places a upper limit on the amount of entropy that a given volume of space may contain. This limit was described by Jacob Bekenstein who tied it quite closely to the Black Hole Event Horizon. Put simply, black holes hold the maximum entropy allowed for their volume. If you...
  3. Ahmedbadr132

    Do all bactriophages cross the blood brain barrier?

    Hi Bactriophages can cross the blood brain barrier but do all of them cross? They are very diverse.
  4. qnach

    A Differential cross section, double differential cross section, triple...

    There are differential cross section, double differential cross section, triple DCS. What are the difference, and why is the names? Thanks.
  5. B

    Python Problem with scikit-learn metrics in K-fold cross validation

    Hello everyone, In my implementation of a K-Fold Cross Validation, I find a difference between the accuracy calculated during each training and the average accuracy calculated through the metric functions of Scikit-Learn. This is my code for the K-Fold Cross Validation and for the calculation...
  6. C

    Deriving algebraic definition of cross product

    So far, I have got the equations, ##u \cdot (\vec u \times \vec v) = 0## ##u_1a + u_2b + u_3c = 0## ##v_1a + v_2b + v_3c = 0## Could some please give me some guidance? Many thanks!
  7. Ranku

    I Cross Section & Mass: Is There a Relation?

    In the sentence "WIMP-nucleon cross sections of 1.2x10-47cm2 at 1 TeV/c2 WIMPs", there is a relationship between cross section and mass. Is there a general formula that relates the two quantities, in that if there is a certain cross section that means it will be associated with a certain mass?
  8. Haorong Wu

    MATLAB Can Light Rays Cross Near a BH? - Simulated w/ Matlab

    Hi. I use Matlab to simulate that two parallel light rays pass near a Kerr BH. The angular momentum of the BH points to the ##z## direction. The ##z## components of the start points of the two rays are ## 1\times 10^3 ~\rm{m}## and ##- 1\times 10^3 ~\rm{m}##, respectively. The result, as shown...
  9. simonjech

    I Lorentz invariant phase space and cross section

    Can someone please explain to me how can we obtain this integral in eq. 5.27 from eq. 5.26? I quite do not understand how is it possible to make this adjustment and why the (p_(f))^2 appeared there in the numerator and also why a solid angle appeared there suddenly.
  10. N

    Delay estimation using cross correlation

    Hi Suppose there are two continuous signals of same frequency say 4 KHz. The time corresponding to its one cycle is around 250 us. If we delay one signal by 4010 us (i.e >> one cycle delay), can we use cross correlation techniques to estimate this delay accurately? Thanks
  11. greg_rack

    Engineering Analyzing Shear & Bending on Idealized Cross Section

    As you can see from the picture, the cross section to analyze is idealized and the boom areas resulting from this are given. For POINT A) all I did was: for determining the shear forces, integrating the shear flows over the sides to compute the vertical and horizontal contribution of each side...
  12. Kostik

    A Static Gravitational Field: Why Must ##g_{m0} = 0##?

    In Dirac's "General Theory of Relativity", he begins Chap 16, with "Let us consider a static gravitational field and refer it to a static coordinate system. The ##g_{\mu\nu}## are then constant in time, ##g_{\mu\nu,0}=0##. Further, we must have ##g_{m0} = 0, (m=1,2,3)##." It's obvious that...
  13. C

    Difference between scalar and cross product

    Hi! For example, how do you tell whether to use the scalar or cross product for an problem such as, However, I do know that instantaneous angular momentum = cross product of the instantaneous position vector and instantaneous momentum. However, what about if I didn't know whether I'm meant to...
  14. C

    Explaining the Cross Product for Two Vectors

    Hi! For this problem, The solution is, However, I don't understand their solution at all. Can somebody please explain their reasoning in more detail. Many thanks!
  15. greg_rack

    Ranking "by eye" bi-material cross sections for strength/stiffness

    Howdy guys, Say we have been given the four thin-walled cross sections below loaded in pure torsion, where the material in black, titanium, has E=100GPa and the one grey one, aluminum, E=75GPa(no clue why Es are given, as I would have expected the shear modulus, G... maybe it is expected to use...
  16. J

    Understanding the Dot Product and Cross Product in Vector Calculations

    Could anyone explain the reasoning from step 2 to step 3? Specifically, I don't understand how to find the product of a cross product and a vector - like (v1 · v2)v1 and (v1 · v3)v1. I'm also confused by v1 × v3 + (v1 · v3)v1 -- is v1 × v3 = v1v3? How would this be added to (v1 · v3)v1? Thank you.
  17. T

    Biology Draw the genetic cross for the given pedigree

    I have tried every possible combination to come up with the cross diagram to no avail Your help is needed please😩😩😩
  18. tbn032

    B Confusion about the angle between two vectors in a cross product

    The magnitude of cross product is defined of vector A⃗ and B⃗ as |A⃗×B⃗|=|A⃗||B⃗|sinθ where θ is defined as the angle between the two vector and 0≤θ≤π.the domain of θ is defined 0≤θ≤π so that the value of sinθ remains positive and thus the value of the magnitude |A⃗||B⃗|sinθ also remain positive...
  19. LUFER

    What is the Electromagnetic Cross Section in this plasma deposition process?

    What is Electromagnetic Cross Section? (shock section) Hello, I have a question regarding the manufacturing process of electronic components in the case of the silicon deposition and corrosion process. My biggest doubt is the behavior of the plasma interacting in the reactor, I don't know if...
  20. P

    Four Snails Traveling on a Plane -- Do they cross paths?

    Since the snails are all in the same plane and their paths are not parallel, shouldn’t the solution simply be yes since the non-parallel lines in the same plane will intersect at some point? This answer seems too simple so I’m unsure if I‘m missing out on a detail.
  21. karmion

    A Cross section-temperature equivalence

    It's assumed that interaction rate between a species of particule m and l is expressed as: Γm=<nlσv>, where nl is the density of the species l, σ the cross-section of species m (=probability of interaction) and v the relative velocity between the two particles. It's also assumed that...
  22. A

    B Black Hole Event Horizon: Atom Effects & Wave Detection

    Are the atoms of objects ripped off when they cross the event horizon? Does a metal rod that partially crosses the event horizon maintain its lattice structure of atoms? If I put a sound wave generator on the end of the bar that has crossed the event horizon how far can the waves be detected?
  23. Anava1001

    A Normalized differential cross section

    Hello, I know that this question might be a bit silly but I am confused about plotting a normalized differential cross section. Suppose that I have a histogram with the x-axis representing some observable X and the y-axis the number of events per bin. I want the y-axis to show the normalized...
  24. T

    A Reason out the cross product (for the moment): a skew symmetric form

    I am sure you are all familiar with the cross product in 3D space. i cross into j gives k. Cyclic Negative, if reversed, etc. I am sure you are all familiar with the definition as: norm of the first vector, norm of the second, sine of the angle, perpendicular (but direction using right hand...
  25. neilparker62

    B Cross section (?) of Great Pyramid from drone footage

    Following is a frame carefully chosen from this drone footage. At about 0:29 into the video the drone is directly in front of one of the four faces (if you know Cairo, you will know which one) and moving from left to right. At that point I have paused and 'frame-stepped' till the moment before...
  26. Garlic

    I Cyclic rotation of the cross product involving derivation

    Dear PF, so we know that cross product of two vectors can be permutated like this: ## \vec{ \alpha } \times \vec{ \beta }=-\vec{ \alpha} \times \vec{ \beta} ## But in a specific case, like ## \vec{p} \times \vec{A} = \frac{ \hbar }{ i } \vec{ \nabla } \times \vec{A} ## the cyclic permutation of...
  27. kuruman

    B A "no hands" rule for the cross product (requires literacy)

    Although it is considered unwise to judge a book by its cover, a book's cover is still useful for finding the direction of the cross product ##\mathbf{A}\times \mathbf{B}## between two given vectors. Being able to read is all that is needed. Here is a detailed procedure. Step 1. Move one...
  28. M

    Feynman rules and the tree level cross section of two scalar fields

    Hi there. I'm trying to solve the problem mentioned above, the thing is I'm truly lost and I don't know how to start solving this problem. Sorry if I don't have a concrete attempt at a solution. How do I derive the Feynman rules for this Lagrangian? What I think happens is that in momentum...
  29. U

    Vectors in yz and xz plane dot product, cross product, and angle

    I tried to find the components of the vectors. ##a_y =2.60 sin 63.0 = 2.32## and assuming the z axis would behave the same as an x-axis ##a_z =2.60 cos 63.0 = 1.18## ##b_z =1.30 sin 51.0 = 1.01## making the same assumption ##b_x =1.3 cos 51.0 = 0.82## I now think I should have switched these...
  30. A

    I Time derivative of the angular momentum as a cross product

    I am trying to find the equations of motion of the angular momentum ##\boldsymbol L## for a system consisting of a particle of mass ##m## and magnetic moment ##\boldsymbol{\mu} \equiv \gamma \boldsymbol{L}## in a magnetic field ##\boldsymbol B##. The Hamiltonian of the system is therefore...
  31. grotiare

    Engineering Question about max stress on circular cross section with two moments

    I couldn't fit in the title, but this is with a hollow circular cross section So currently I am trying to figure what occurs when two, perpendicular bending moments are applied to a hollow circular cross section (one about the z axis, and the other about y). I know that if I was dealing with a...
  32. morrobay

    COVID Cross Reactive Covid 19 Immunity From Exposure to Endemic Coronaviruses

    https://onlinelibrary.wiley.com/doi/10.1002/jmv.26958. Since the majority of Covid cases are mild or Asymptomatic one possible factor could be existence of cross immunity in a population as a result of previous exposure to other Endemic Coronaviruses.
  33. Johnstonator

    What would be the ideal cross section of an axially loaded cantilever beam?

    Pretty much the title. Just some brain teasers I'm trying to figure out. I can't think of how a cross section would come into play when it comes to axial loading. Buckling? Since the critical force for buckling is proportional to moment of inertia, so theoretically if I have a high moment of...
  34. D

    I Question about the vector cross product in spherical or cylindrical coordinates

    Hi If i calculate the vector product of a and b in cartesian coordinates i write it as a determinant with i , j , k in the top row. The 2nd row is the 3 components of a and the 3rd row is the components of b. Does this work for sphericals or cylindricals eg . can i put er , eθ , eφ in the top...
  35. greg_rack

    Basic vector operations, using cross and dot product

    Hi guys, I am losing my mind over this passage... I cannot understand how to get from the first expression with the cross products to the second ##\dot{\textbf{r}}(\textbf{r}\cdot \textbf{r})-\textbf{r}(\textbf{r}\cdot\dot{\textbf{r}})##
  36. B

    Round vs Square cross section tubing

    I want to make some beaching legs for my 30ft, 9T yacht... these are supports either side of the yacht that keep it upright when the tide goes out and it sits on its keel without falling from one side or the other. My question is this, would it be stronger to use sguare or round tube to do this...
  37. A

    I Cross Product in E_u: Explaining Gourgoulhon's Text

    I study from Gourgoulhon's text 'special relativity in general frames', I have some difficulty to understanding Chapter 3 Page 84. I already learn that there exist a orthogonal projection mapping ##\bot_{u}:E \rightarrow E_u(P)## from the vector space ##E \cong R^4## to the subspace ##E_u(P)##...
  38. Amy_93

    I Statistic uncertainties in cross section plots - how to calculate?

    Hi there, I hope I chose the right forum for my question. So, basically, I'm doing an analysis measuring the number of signal particles in a certain momentum bin i, and doing two corrections: Nsig, i=M*(Nmeas, i-Nbkg, i) Here, M is a matrix covering PID correction and PID efficiencies, and...
  39. Buckethead

    Stargazing Is There a Common Pattern in Einstein Crosses?

    This is probably just a coincidence, but I happened to notice while looking at Einstein crosses an unusual pattern common to these four images. I was looking for more but it turns out there may not be as many crosses as I originally thought. Must be rare. The pattern is that of the 4...
  40. E

    B What is the cross product of two vectors?

    I understand that dot product gives us a number and cross product gives a vector. Why is this vector orthogonal to the others two, and why it has magnitude |a|*|b|*sinΘ? How to use cross product? What does it give to us?
  41. D

    I The 1/v law for U-235 cross section

    The cross section for fission of U-235 is much higher for slow, thermal neutrons than for fast neutrons, for which it is similar to the geometric area. The cross section for slow neutrons seems to decrease empirically like 1/v where v is the velocity of the neutron. What is the qualitative...
  42. greg_rack

    Vector cross product anti-commutative property

    That may sound really silly, and that may be due to my lack of understanding of the operations itself, but: if ##|\vec{a}\times\vec{b}|=|\vec{a}|\cdot|\vec{b}|sin\theta##, being ##\theta## the angle between the two vectors, how could ##\vec{b}\times\vec{a}## be different? Wouldn't it be just the...
  43. greg_rack

    Calculating vector cross product through unit vectors

    Writing both ##\vec{U}## and ##\vec{B}## with magnitude in all the three spatial coordinates: $$ \vec{U}\times \vec{B}= (U_{x}\cdot \widehat{i}+U_{y}\cdot \widehat{j}+U_{z}\cdot \widehat{k})\times (B_{x}\cdot \widehat{i}+B_{y}\cdot \widehat{j}+B_{z}\cdot \widehat{k})$$ From this point on, I...
  44. Filip Larsen

    I Rotational invariance of cross product matrix operator

    Given that the normal vector cross product is rotational invariant, that is $$\mathbf R(a\times b) = (\mathbf R a)\times(\mathbf R b),$$ where ##a, b \in \mathbb{R}^3## are two arbitrary (column) vectors and ##\mathbf R## is a 3x3 rotation matrix, and given the cross product matrix operator...
  45. F

    A How Are 2D and 3D Cross-Correlations Implemented in Large-Scale Surveys?

    In the context of forecast for large survey, I have to make cross-correlations between 2D (with angular coordinates of Lagrange transformation for GC photometric and Weak Lensing) and 3D (Fourier transform with radial coordinates for GC spectroscopic). For the moment, only cross-correlation...
  46. G

    I How to approach a cross product question

    I am beginning this new general physics course and I have encountered a question involved with what I assume to be cross products, a topic that I have very little experience with. I am not looking for a direct answer to the problem but advice on what steps should be taken in order to learn how...
  47. Haorong Wu

    I Where does this formula for absorption cross section come from?

    My professor gave us a formula for absorption cross section, but he said he did not remember where he found it. The formula is given by $$\sigma_a =\frac {1} {| \mathbf E_i|^2} \int_V k \epsilon^{''}_r | \mathbf {E} |^2 dV = k \epsilon^{''}_r |\frac 3 {\epsilon_r +2}|^2 V.$$ Where does...
  48. F

    A Cross correlations with 2 probes: Approximation of a 2D + 3D synthesis

    I am interested, in the context of my work, in the cross correlations between a spectroscopic probe (which gives a 3D distribution of galaxies with redshifts, which is also called spectroscopic Galaxy clustering, GCsp) and a photometric probe (which gives an angular distribution, that is to say...
  49. R

    A Compton Recoil and the Electron Differential Cross Section

    Hi folks, My understanding of the Compton Effect is that maximum energy transfer to the electron takes place when the photon scattering angle is 180 degrees. For the following please reference Evans "The Atomic Nucleus" ...
  50. I

    Connecting Two 30x10mm2 Earth Busbars: Min. Conductor Cross Section

    I have two 30x10mm2 Earth busbars in switchboard, both are placed on insulators, but connected through various parts of switchboard (ground terminal, rails, door, mounting plate...) What is the minimal conductor cross section allowed for connecting this two busbars directly?