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. S

    Confused with Right hand in context of Cross Products

    This is not a homework problem, but pertains to the class (Calculus II) that I am taking. I am very confused about how to think intuitively about determining orientation of a cross product. My understanding of the right hand rule in determining the orientation of the third axis is that...
  2. U

    Dynamics Moments - Linear Algebra / Cross Product

    Some background: I am self studying dynamics and I have encountered a fundamental problem with either my understanding of linear algebra, or I am just plain dumb. So, I print screened the page of the book we're on. Now let me try to reduce some ambiguity in my question, I have a general...
  3. J

    Cross product between unit vectos

    I have a nice table that shows the dot product between unit vectos (see annex). I'd like know how is the cross product between unit vectos of all basis. Do you have a table with such information?
  4. J

    Collision Mechanics and Differential Cross Section

    Homework Statement The problem concerns the collision of a particle on a rigid, fixed disk of radius R. The coefficient of friction is zero, and the coefficient of restitution is 0 < ε < 1, such that vperpendicular, final = εvperpendicular, initial . A) Show that tanαincident = εtanαfinal...
  5. J

    An extension of Dot and Cross Product

    I was thinking, if exist a product (cross) between vectors defined as: \vec{a}\times\vec{b}=a\;b\;sin(\theta)\;\hat{c} and a product (dot) such that: \vec{a}\cdot\vec{b}=a\;b\;cos(\theta) Why not define more 2 products that result: \\a\;b\;sin(\theta) \\a\;b\;cos(\theta)\;\hat{d} So, for...
  6. C

    Is the Vector Equation AxB=AxC Only True When A=0 or B=C?

    True or False, if AxB = AxC then either A=0 or B=C. A, B, and C are vectors and I thought this statement would be true. However the answer key says it is not. Why?
  7. Safinaz

    2 -> 2 hadronic production cross section

    Hi all, Could anyone help for calculating the hadronc production cross section for example for tree level : p p > t t~ process, I try to calculate, but the first problem I meet is a negative value of the matrix element amplitude (and so cross section ) and a negative ## \hat{t} ## Mandelstam...
  8. Simon Bridge

    Rod Cross' collisions, sports balls, and silly putty

    A surprising find looking for something else: http://www.physics.usyd.edu.au/~cross/ Somewhat extensive notes on various small-ball sports physics - including material on collision physics and a neat vid of a falling slinky. I've mined: Ball bounce for comparative data for experiments...
  9. E

    Question regarding Lab cross section of spectra

    I'm currently doing some research at the moment for my professor, and he gave me a list of things to look at. Before he had me calculate the "real center of mass cross section." Now, starting at point 0 for publication, he's having me go through and do some other things. In his list of things to...
  10. F

    Interpretation of Cross Section of p,n reaction mb or mb/MeV

    Dear Forum : I'm reading a cross section data of 20MeV proton + 16O reaction from ICRU 63. ( as attachment and link http://ppt.cc/qf-9 ) The total cross setion of (p,n) reaction is 4.372mb However, the cross section of emitting neutron of energy between 0 to 1.5MeV is 0.91 mb / MeV. The...
  11. G

    Applying cross product to some problem

    Hi, So I still not sure how to apply like rhr rule in this setup in problem like the one in the following so I tried to do rhr in order to get the direction but it didn't work out. this is an example from halliday and resnick book. Figure 32-24 shows a wire segment,placed in a uniform...
  12. F

    Schools Subpar GPA; Aspirations for Grad School and cross discipline research

    Hello everyone, I am currently in my third semester at Rutgers University with a declared major in Physics. I aspire to do post-baccalaureate studies. However, my GPA is just "average." I have read through threads where the OP is in a similar situation to mine, and I have found a lot of...
  13. B

    Finding the Position Vector for Opposite and Half Torque on the Y Axis

    First of all I want to thank you for taking your valuable time to help me out. I typically would not ask a homework question, but I have exhausted all other resources in search for an answer to my question. I will do my best to fully summarize my situation and its circumstances, seeing as this...
  14. T

    Cross Product Magnitude and Direction Calculation for Vector v and Vector B

    Homework Statement Find the magnitude of \vec{v} \times \vec{B} and the direction of the new vector. \vec{v}=\left \langle 0,0,20 \right \rangle \vec{B}=\left \langle 1,1,0 \right \rangle Homework Equations |\vec{v}|=\sqrt{0^2+0^2+20^2}=20 |\vec{B}|=\sqrt{1^2+1^2+0^2}=\sqrt{2}...
  15. Safinaz

    What's the Difference Between Cross Sections?

    Hi all, I'd like to more understand what is the difference between when we draw the differential cross section ## \frac{d \sigma ~ (pb)}{dM ~ (GeV)} ##, when we draw ## \sigma ~ (pb) /bin## and the total cross section ## \sigma ~ (pb) ## .. I mean for a process like p p > x x~ (where...
  16. P

    Derive cross product from dot product

    can you show me derive cross product from dot product?
  17. M

    Help taking a cross product of a matrix

    hey all well the title says it all. if i want to take the cross product of two matrices, how do i do it? any help, advice, etc. is very appreciated! thanks
  18. Philosophaie

    Cross product of two 4-Vectors

    How do you take the cross product of two 4-Vectors? \vec{r} = \left( \begin{array}{ccc}c*t & x & y & z \end{array} \right) \vec{v} = \left( \begin{array}{ccc}c & vx & vy & vz \end{array} \right) \vec{v} \times \vec{r} = ?
  19. L

    Expanding triple (cross) product

    Homework Statement Use (the bac-cab rule) to expand this triple product:L = mr x (ω x r) If r is perpendicular to ω, show that you obtain the elementary formula, angular momentum = mvr. (The bold letters are vectors.) Homework Equations A X (B X C) = (A\cdotC)B - (A\cdotB)C...
  20. M

    Cross product to find the area of a triangle

    okay so I know that the area of the triangle is half the area of the parallelogram, ill try using pictures because this is a bit confusing to describe only with words: for example we have this http://farside.ph.utexas.edu/teaching/301/lectures/img243.png and then if we use the cross product of...
  21. B

    What is the cross product of 5k and 3i+4j?

    i have a vector xK where k is the unit vector perpendicular to other unit vectors i and j when i multiply a force which has 5k for instance another which has ( 3 i + 4 j ) i multiply 5k by 3i then 5k by 4j right ? the answer would be ( 15 j - 20 i ) right ?
  22. PsychonautQQ

    Problem Understanding theorm of Cross Product

    Homework Statement My textbook says: The length of the cross product a x b is equal to the area of the parallelogram determined by a and b. How can a length equal and area? They have different units?
  23. PsychonautQQ

    Cross product and Dot product problem

    Homework Statement if v x w = <5,5,-2> (v cross w) and v * w = 6 (v dot w) then what is the tan(θ) between the two vectors v and w? The Attempt at a Solution well I was thinking v x w = |v||w|sinθ as well as v dot w (v*w) = |v|w|cosθ divide one equation by the other...
  24. M

    Would The Cross Product of x and x be z0?

    Just like the title says, would that technically be true? I know the cross product is normal to the plane of the two vectors being crossed, which would make it z. However, since the angle between two vectors is 0, sin (0) = 0...
  25. D

    MHB Vector Analysis: $\varphi$, $\mathbf{v}$, and Their Cross Products

    $\newcommand{\unit}[1]{\hat{\mathbf{#1}}}$ Let $\varphi = F_1h_1$ and $\mathbf{v} = \frac{\unit{u}_1}{h_1}$. Why is $\varphi\nabla\times\mathbf{v} = 0$ but $\nabla\varphi\times\mathbf{v}$ not?
  26. V

    Derivative of Cross Product with Differentiable Functions

    Homework Statement Assume that you are given differentiable function f(t) and g(t). Find a formula for the derivative of the cross product u(f(t)) x v(g(t)). Homework Equations d/dt(u(t) x v(t)) = (u'(t) x v(t) + u(t) x v'(t) The Attempt at a Solution So in this case I was thinking...
  27. A

    Torsion of rectangular cross section rotated at an angle?

    I want to use a rectangular cross section to act as a torsion spring that can be adjusted. The idea is that the adjustment would be made via rotating the rectangular cross section about it's center at an angle theta. I've used parallel axis theorem before, but I don't think that is applicable...
  28. D

    Jerk times velocity cross position

    The problem asked me to prove the following (where \vec{r}, \vec{v}, \vec{a} are the position, velocity and acceleration vectors of a moving particle): \frac{d}{dt} [\vec{a} \cdot (\vec{v} \times \vec{r})] = \dot{\vec{a}} \cdot (\vec{v} \times \vec{r}) I already did so, but my question...
  29. U

    Vector Geometry find cross product.

    Homework Statement Calculate the cross product of (3u+4w)xw assuming that uxv=<1,1,0>, uxw=<0,3,1), vxw<2,-1,-1)Homework Equations Possible Relevant eqation: i) wxv=-vxw ii)vxv=0 iii)vxw=0 if and only w= λv for scalar λ or v=0 iV)(λv)xw=vx(λw)=λ(vxw) V) (u+v)xw= uxw+vxw ux(u+w)=uxv+uxw The...
  30. G

    Why Is the Cross Product Perpendicular to Its Constituent Vectors?

    Why does the cross product produce a vector and why is that vector perpendicular to the other vectors? I understand how to calculate a cross product, but why for instance is the cross products of two vectors another vector that is perpendicular to it. Can you prove or explain this to me in...
  31. S

    Positron cross section with H,D,T

    I have a question about cross section probability for a positron (e+) to interact with the electron (e-) that would be bound to three different atomic systems (1) hydrogen atom: H(e-), (2) deuterium atom: D(e-), (3) tritium atom: T(e-). My hypothesis is that a positron (e+) would have the...
  32. O

    Calculating x for Perpendicular Vectors A and B: Dot and Cross Product Homework

    Homework Statement A=(x,3,1) ,B=(x,-x,2) Determine the value of x if the vector perpendicular to A and B is given by C=(10,-4,-4) Homework Equations The Attempt at a Solution Find A cross B , let A cross B be D . Then D cross C = zero (since they are perpendicular to both A and...
  33. P

    Understanding the Correct Representation of the Cross Product of Vectors

    a and b are two vectors and x is the angle between them. ||axb|| = ||a||||b||sinx ------(1) ||axb|| = ||a||||b||||sinx|| ------(2) which one is correct? why?
  34. O

    How to do cross product if I have got only two coordinate?

    a =(x,y), b =(h,k) a cross b =? I have idea what to type on google. Is that doing like matrices , a cross b = xk-hy? thanks.
  35. C

    Cross Product of vectors in vector mechanics by beer and johnston

    Hi, I was reading vector mechanics by beer and jhonston. I came across the equation wherein the cross prodcut of two vectors P and Q is given. It says P x Q = P x Q` . I am not bale to understand how dis is possible. Because as the vector Q changes even the angle teetha will change then how...
  36. I

    Why is the right hand rule for cross product?

    so, the magnitude of the cross product represents the area or volume enclosed by any 2 or 3 vectors respectively, but what does the direction represent? i get that the general direction is one that is perpendicular to all the vectors, but what does the actual direction represent? ie, why the...
  37. K

    Calculation of neutron transport cross section

    I have a book on nuclear reactions which details the mean free paths for thermal neutron scattering as: 0.37cm for water and 2.2cm for heavy water The transport cross sections are listed as 0.45cm for water and 2.6cm for heavy water. Does anyone know how to calculate these from the thermal...
  38. J

    Why is the W cross section so much larger than the Z cross section?

    I had a look at the production cross sections for W/Z at hadron colliders. These differ as a function of energy with the W x-sec being consistently ~10 times larger than the Z cross sections. Why is the W cross section so much larger? I think the coupling strength is similar and the mass...
  39. C

    Compression and bending on a cross section,how to make sure its static

    The problem is the following, i have a rectangle as a cross section of steel, which is bended and compressed.. i want to use the equilibrium equations to make sure its static, but since the compressive force and the traction force aren't equal, the equilibrium equations make no sense here's a...
  40. L

    E+e- -> gamma f0 -> gamma pi0 pi0 cross section with VMD

    e+e- --> gamma f0 --> gamma pi0 pi0 cross section with VMD Homework Statement Find the cross-section of ##e^+e^- \to \gamma f_0(980) \to \gamma \pi^0 \pi^0## using the vector meson dominance model. Homework Equations Some Feynman's rules: The photon propagator is -i...
  41. D

    Why does the cross section drop between resonances?

    Hello. When you have a plot of the cross section in function of the centre of mass energy of an e+e- -> hadrons collision, you get a graph with a few peaks which are due to the resonances (ρ, ω, J/ψ...). But I don't understand why at a resonance, the cross section goes up? Or other way...
  42. R

    What will be the cross section area of rod?

    If a metal rod of 20 cm is charged with 10 μC, then what should be its cross section area so as to prevent electric discharge (electric breakdown) ?
  43. S

    Deriving del cross A in Electrodynamics

    Hello, I am trying to derive the equation for the B-field due to a moving charge. ~ Griffiths Chapter 10, equation 10.66. I have been trying to “do” the del cross A and simplify . Things get messy and I am uncertain on some of my vector operations. In searching the internet I find...
  44. S

    Difference in thermal n cross section for Be-9 and B-10

    I have a question. From this government reference: http://www.ncnr.nist.gov/resources/n-lengths/ the thermal neutron cross section for stable isotope Be-9 = 0.0076 barns. This means Be-9 is not expected to absorb a thermal neutron, the probability of this is very, very low. The Be-9...
  45. G

    Cross product of complex vectors

    How is computed the cross product of complex vectors? Let ##\mathbf{a}## and ##\mathbf{b}## be two vectors, each having complex components. $$\mathbf{a} = a_x \mathbf{\hat{x}} + a_y \mathbf{\hat{y}} + a_z \mathbf{\hat{z}}$$ $$\mathbf{b} = b_x \mathbf{\hat{x}} + b_y \mathbf{\hat{y}} + b_z...
  46. K

    Is Dropping Out of College for a Business Worth the Risk?

    Hello to all, I have posted before about my interest in becoming a chemical engineer because I am very interested in starting my own brand of cleaning chemicals. Im contemplating if i should drop out of my engineering program in order to work 80 hours a week to save money to start business, or...
  47. E

    Volumes of Solids with Known Cross Section Project

    I'm trying to get started on this project but am totally confused about how to find the volume of the solid. All the information I was given was the following: y= √x boundaries: 0,9 cross sections: isosceles right triangle how the hell do I get started?!
  48. S

    Griffiths Chapter 10 del cross position vector

    I am working through chapter 10 of Griffith’s electrodynamics (for fun and in my spare time). While I don’t have a formal bucket list, getting to an understanding of how Newton’s third law is not as straightforward for electrodynamics has been on my mental bucket list. I am an engineer not a...
  49. A

    Classical Limit formula for differential cross section for Hard Sphere

    I am looking for the derivation to an approximation formula for the differential cross section for hard sphere scattering in the limit of high energy. The paper that mentioned this had referred to Methods of Theoretical Physics, PM Morse and H. Feshbach page 1484 but I have no access to the...
  50. F

    A Beam of rectangular cross section 200mm deep and 100mm wide

    Homework Statement Please visit my flickr link for a scanned image of the problem statement. http://www.flickr.com/photos/93763273@N05/8815418518/lightbox/ Homework Equations M/I = σ/y = E/R This is the flexure or bending formula. The Attempt at a Solution a) = 8.333 kN...
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