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. P

    Finding B Using Cross Product in Magnetic Force Equation

    Homework Statement find B from F=q(v X B), where F is magnetic force, q = charge, v = velocity, B = magnetic field. Carrying out 3 experiments, we find that if v_1 = i, (F/q)_1 = 2k - 4j v_2 = j, (F/q)_2 = 4i - k v_3 = k, (F/q)_3 = j - 2i where i,j,k are the unit cartesian vectors This...
  2. J

    Electron-impact ionization cross section

    I'm calculating an ionization cross section in partially ionized plasma, with taking into account of correlation effects. I'm trying to do it with help of variation phase method. Please, help me to find some link to useful articles.
  3. H

    When does the particle first cross the negative x axis?

    Suppose that a particle's position is given by the expression in the attachment Explain: 1. When does the particle first cross the negative x axis? 2. Find the particle's velocity as a function of time. Express your answer using unit vectors.(e.g., A i_unit+ B j_unit, where A and B...
  4. N

    Vector Cross Product Homework: Solving AxB with B values of 8i+16j and -8i-16j

    Homework Statement Given that A = 2i + 4j, evaluate each of the following. (Hint: This question can be answered without computation.) (a) What is AxB when B = 8i + 16j? (b) What is AxB when B = -8i - 16j? Homework Equations AxB=(Axi + Ayj) x (Bxi +Byj) =(AxBx)(i x i)...
  5. D

    Solving Cross Product w/ Determinants: Setting Up Equations

    I'm having trouble relating the cross product form |a||b|sin(theta) to its component form (a1b2 - a2b1) ... and so on... I know how to do this mathematically so please don't just suggest some proof that I can find in every textbook... The component form involves the solutions to equations...
  6. J

    How Is Current Calculated from Electron Flow Rate?

    1. How do you find the current if it tells you how many electrons pass through cross section of a conductor each second 2. ... 3. ...I don't know the first thing to do about this. Just the number of electrons make me think of the equation Q = Ne ..but charge doesn't have to do with...
  7. E

    Cross Correlation Homework: Measuring Delay

    Homework Statement A signal x(t) is transmitted and received back as y(t) and sampled in the receiver, so we get a DT signal y[n] = ax[n-D] + w[n], where w[n] is noise baiscally i need to explain how we can measure the time delay by computing crosscorrelation Ryx(l). My undestanding is...
  8. J

    Why is AXB not equal to BXA?

    Homework Statement Show that AXB is not equal to BXA No variables given..just this equation Homework Equations The Attempt at a Solution I don´t know how to start...the only thing I know so far is that AXB is equal to -BXA
  9. M

    Cross product and force on a charge due to applied magnetic field.

    Homework Statement I hope I am not posting this question at the wrong place, but can someone explain to me the vector product rule, or cross product rule. I don't seem to get the hang of it. Why I am asking this is because I want to know how force on a moving charge due to an applied...
  10. T

    Energy and cross sections

    I was wondering whether there's any interactions or productions that has cross section that doesn't only increase monotonously with energy, but has a drop somewhere at certain energy scales ?
  11. quasar987

    Definition of cross product in Spivak's 'Calculus on Manifolds'

    Homework Statement In Calculus on Manifold pp.83-84, Spivak writes that "if v_1,...,v_{n-1} are vectors in R^n and f:R^n-->R is defined by f(w)=det(v_1,...,v_{n-1},w), then f is an alternating 1-tensor on R^n; therefore there is a unique z in R^n such that <w,z>=f(w) (and this z is denoted v_1...
  12. E

    Find unit vector and cross product

    Homework Statement Given the two vectors written in component-unit vector form below: D = 3\hat{i} - \hat{j} E = 2\hat{i} + 4\hat{j} a.) Find the unit vector in the same direction as D b.) Find the cross product of D x E c.) Write the vector D in magnitude direction form Homework...
  13. B

    News The costs of a cross country trip

    After I graduate from college I planned to drive across the United States on my little chevy and tour all the US landmarks and experience the taste of the regional food while on the way to graduate school. My only primary worry is how expensive it will be to travel across the country if from...
  14. V

    Cross Sections for Neutron Scattering in Different Frames

    This is probably a very dumb question, but I'm stuck with it. The cross sections one finds on http://www.nndc.bnl.gov/sigma/ as a function of incident energy, is that energy given in the lab frame or in the cog frame ? For heavy a nuclide, this doesn't matter, but for hydrogen for instance ...
  15. N

    How to Differentiate Cross Product?

    Hi all, I have a qustion. dB/ds= -TN, dU/ds= KN (1) N= U x B (2) dN/ds=TB-KU (3) How Eq.(3) can be obtained from Eq.(1),(2)? Have a nice day!
  16. S

    Cross Product in Uniform Circular Motion

    Homework Statement A centripetal-acceleration addict rides in uniform circular motion with period T = 3.22 s and radius r = 3.00 m. At one instant his acceleration is a = (7.00 m/s2) i + (-9.00 m/s2) j. At that instant, what are the following values? (b) r X a The Attempt at a...
  17. K

    Young's Modulus Calculation for Nylon Rope Cross Sectional Area

    Homework Statement I'm working on a problem that is asking me to find Young's Modulus. I have the right formula and everything that I need but I can't seem to figure out how to find the cross sectional area of a nylon rope. The rope is 21 m long and 1.4 cm in diameter. Homework...
  18. L

    Help with derivation - involves cross & dot products

    Hello, I'm reading a classical mechanics book. In it, they show a derivation of the centrifugal force equation: \vec{ F_{\textrm{cf}}} = -m \vec{ \omega } \times \left( \vec{ \omega } \times \vec{ r } \right) I understood the derivation up to that point. However, they have a couple additional...
  19. L

    Where Can I Find Resources for Cross Sections and Decay Rates?

    Hy guys, i don't know if this is the best place to post this... so this is my question: where i can found a good resource for cross sections and decay rate? i mean a book with many calculated cross sections or web sites. thank you.
  20. T

    Calculating Cross Product in 3D and 7D

    Why is it possible to take the cross product in only 3 and 7 dimensions?
  21. Jorrie

    Einstein Cross vs. Ring: Understanding the Alignment of Quasar G2237+030

    The Einstein cross (G2237+030) shows 4 reasonably symmetrically spaced images of the very distant quasar, indicating that our alignment with the galactic nucleus to quasar line is fairly good. How is that it does not show an Einstein ring instead of the cross?
  22. N

    What is the unit vector perpendicular to (2,1,-3) and (-1, 7, 4)?

    Use two methods to determine a unit vector perpendicular to both (2,1,-3) and (-1, 7, 4) Using Cross Product: Let v be a perpendicular vector to the given vectors v = a*b = (2,1,-3)(-1,7,4) =((1)(4)-(7)(-3), (-3)(-1)-(4)(2), (2)(7)-(-1)(1)) =(4+21, 3-8, 14+1) =(25, -5, 15) = (5, -1...
  23. I

    Proof of Dot and Cross Product of Arbitrary Vectors with Pauli Spin Operator

    I need to show: (\mathbf{\sigma} \cdot \mathbf{a})(\mathbf{\sigma} \cdot \mathbf{b})=\mathbf{a} \cdot \mathbf{b} I + i \mathbf{\sigma} \cdot (\mathbf{a} \times \mathbf{b}) where a and b are arbitrary vectors, sigma is the pauli spin operator. I was just wondering what the dot product...
  24. C

    Proof 3d vector cross products

    2 questions i have; 1. proove that; p x ( q + r ) = p x q + p x r 2. and p x ( q x r ) = ( p x q ) x r where; p = p1i + p2j + p3k q = q1i + q2j + q3k r = r1i + r2j + r3k
  25. S

    What is the relationship between the exterior and cross products?

    How are the exterior products and the cross products related? Wikipedia says: "The cross product can be interpreted as the wedge product in three dimensions after using Hodge duality to identify 2-vectors with vectors."
  26. K

    Using Cross Products To Find Electric Field Vector

    A charged particle moves through a region of space containing both electric and magnetic fields. The velocity of the particle is v = (3.3 x 10^3 m/s) x + (2.7 x 10^3 m/s) y and the magnetic field is B = (0.81 T) z. Find the electric field vector E necessary to yield zero net force on the...
  27. A

    Differential equation with cross product

    ok, i don't know what to do with something like this: (d^2R/dt^2 ) + (dR/dt) x B = 0 where the capitals are vectors (sorry i suck at latex). R is a position vector in x-y plane and B is in the z-direction. do i split this into equations for x and y directions separately and solve them...
  28. T

    Cross product in spherical coordinates

    Hi guyz, I have a small question, In spherical coordinates if we define 2 vectors such as magnetization of a shell M(r,phi,theta) and the magnetic field H(r,phi,theta) As we know the cross product between them is written in the determinant: (Capital means unit vectors) det[(R,r...
  29. Z

    How to prove the width of a resonance using the cross section of a S wave?

    Homework Statement The total cross section of a S wave is given by the following equation Sigma=(pi/k)*(b^2)/((E-En)^2+(b/2)^2)) prove that b is the width of the resonance. Homework Equations Nothing that is the only thing The Attempt at a Solution I already solved the question...
  30. K

    Understanding Cross Product Derivatives for Vector Functions

    hi all. my homework question is what is the derivative of: [(a + t * b) x (a + t * b + t^(2) * c)] a, b, and c are vectors, and t is a constant. * is multipy, ^(2) is squared, and x is cross product. i've been working on it for hours and i have no idea what to do. there's another similar...
  31. D

    Dot product cross product, where did they come from?

    While taking linear algebra I never really understood where the dot and cross product came from. It seemed that they were just randomly defined. I know that the dot product is an inner product but why is it defined as: \vec v \cdot \vec u = v_1 u_2 + v_2 u_2 ? why not \vec v \cdot \vec u =...
  32. D

    Cross section for scattering of gauge bosons and Majorana neutrinos

    For my diploma thesis I must provide a calculation that reproduces the results given on page 46 of the paper hep-ph/0309342 . For those who do not want to look it up, I briefly explain what it is about: It concerns the two-body scattering processes (1) N + V => L + H, (2) N + L => V + H, (3) N...
  33. H

    Understanding the Meaning and Importance of Cross Product in Rotational Motion

    I didn't use the template, because I am not having difficulties with a problem. I am just starting to study rotational motion and there it appears the cross-product. I don't like to memorize formulae that I don't understand it's meaning. Why is \vec a \times \vec b} defined mathematically...
  34. P

    Cross Sectional Area to Newtons

    [b]1. When the hot water in a certain upstairs bathroom is turned on, a series of 18 "ticks" is heard as the copper hot-water pipe slowly heats up and increases in length. The pipe runs vertically from the hot-water heater in the basement, through a hole in the floor 5 m above the water heater...
  35. P

    Vector space for cross products?

    What vector space are cross products done in?
  36. M

    Hard nuclear physics cross section problem

    In a scattering experiment, an aluminium foil of thickness L = 10E-6 m is placed in a beam of intensity of 6E12 particles per second. The differential scattering crosss section is known to be of the form. \frac{d\sigma}{d\Omega} = A + Bcos^2 (\theta) where \theta is the...
  37. V

    Finding torque (vector cross product)

    A particle position is described by position vector r = 3i + 2j and the force vector i - 2j acts on the object. 1) Find the torque about an axis through the origin and perpendicular to the xy plane. Draw the two vectors to check your torque direction. I used the right hand rule and found...
  38. P

    How to Solve Cross and Dot Product Problems with u, v, and w?

    Ok, this one has really got me... Suppose that u \centerdot (vXw) = 2. Find (a) (uXv) \centerdot w (b) u\centerdot(wXv) (c) v\centerdot(uXw) (d) (uXv)\centerdotv Once I understand the what to do with the information given, I am sure the rest of the problems will fall into place...
  39. S

    Possible Generalization of Cross Product?

    In R^3 it is easy to compute the cross product, and i know how to compute it in higher dimensions using wedge product and the hodge star, which shows that it only exists in 3n dimensions. My question is given two vectors in C^3 (complex), is there a neat way to find one perperdicular to...
  40. C

    Self pollination & Cross pollination

    My book says self pollination maintains the parental characters or purity of the race indefinitely and is used to maintain pure lines for hybridization experiments. How can that be true. Coz, meiosis takes place in micro & mega spore mother cells. So there is crossing over which will lead to...
  41. T

    Solving x=(x x A)+B: Cross Product Solution?

    I am supposed to solve this explicitly for x: x=(x x A)+B where all variables represent vectors. I moved the B vector to the other side and I was thinking i can take a cross product of something with each side to isolate x but do not know what works here, i tried crossing both sides with...
  42. A

    Is cross section is proportional

    If I show something that a cross section is proportional to: 1 / (16p^2 sin^4( x) + 8mpsin^2 (x) + m^2) does it imply that the cross section is proportional to 1 / sin^4 (x) as well?
  43. R

    Strain-stress, cross sectional, elongation

    Hey guys, I will admit that I am having extra troubles on this chapter and I don't understand most of it so be gentle :\. Anyways I realize these problems are porbably easy but here they are: 1) A Load of 140,000 N (31,500lbf) is applied to a cylindrical specimen of a steel alloy that has a...
  44. S

    Cross Products and Determinants

    Is the fact that \vec{a}\times\vec{b} = \det \begin{bmatrix}\hat{e}_1& \hat{e}_2 & \hat{e}_3 \\ a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \end{bmatrix} just a coincedence (ie. a mneminic device) or does it have some deep mathematical significance? edit: Also, is the cross product, like the dot...
  45. T

    Dot and cross product problem

    Hello, my problem is as follows: Given that A and B are known vectors, and A \cdot C=u is a known quantity, and A \times C=B Express C in terms of A,B, u, and the magnitude of A So far what i have done was use the definition of the dot product as AC cos \theta=u, and cross product as AC...
  46. P

    Understanding Vector Cross Product: Finding the Angle Between Two Vectors

    This is the question: Two vectors A and B have magnitude A = 3 and B = 3. Their vector product is A X B = -5k+2i. What is the angle Between A and B. OK so I'll start with what I do know. I do know that the cross product is the magnitude of A times magnitude of B times sin theta of B. I end...
  47. P

    How to identify the ratio of the cross sectio of capture and recombination

    Sometimes we need to know the ratio of the capture section and recocmbination cross section of the electron or hole. for example, to identify the mechanism of phosphors, it's very important to know the ratio to analyze the process of luminescence. The question is how we identify the ratio, from...
  48. P

    Time needed to cross river - depends on flow of the water?

    When you swim across a river does the time to reach the opposite shore depend on the rate of flow of the water? Defend your answer
  49. K

    Will Dmitri's Thesis Defence Be a Success Tonight?

    I have my thesis defence tonight at 17h CET. :biggrin: If you like, I've put the presentation online http://www.geocities.com/dimitri_terryn/Presentatie_thesis.ppt It's in Dutch, but I will translate it when I have the time (i.e. after graduation).
  50. X

    Proving Real Cross-Ratio with 4 Distinct Points in Complex Plane

    Can some one help me out here, I'm stuck on the following problem: show that four distinct points z_i , i=1,\ldots,4 in \hat{\mathbb C} lie on a circle in \hat{\mathbb C} if and only if the cross-ratio \left[ z_1,z_2,z_3,z_4 \right] is real. So, I know we can write the...
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