Cross Definition and 1000 Threads

  1. 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 ?
  2. 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?
  3. 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...
  4. 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...
  5. 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?
  6. 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...
  7. 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...
  8. 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...
  9. 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...
  10. 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...
  11. 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...
  12. 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...
  13. 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?
  14. 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.
  15. 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...
  16. 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...
  17. 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...
  18. 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...
  19. 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...
  20. 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...
  21. 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...
  22. 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) ?
  23. 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...
  24. 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...
  25. 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...
  26. 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...
  27. 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?!
  28. 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...
  29. 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...
  30. 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...
  31. M

    Question involving cross product and planes

    Homework Statement Take P;Q and R three points of R 3 not on the same line. If a = OP , b = OQ and c = OR are the position vectors corresponding to the three points, show that a x b + b x c + c x a is perpendicular to the plane containing P;Q and R The Attempt at a Solution I don't...
  32. A

    How Does Dust Grain Size Compare to Wavelength in Scattering Light?

    Hey everyone, So I've been killing myself trying to find a good reference that talks about the wavelength dependence of dust grains when the size of the grain is about the size of the incoming light, or s~lambda. I have numerous references for when s<<lambda (absorption dominates with a...
  33. B

    The thermal activation cross section of H-3,C14

    I am doing a research on activation radionuclides resulting from thermal neutron(2200 m*s-1 or 0.0253eV) capture. The activation cross section of some nuclides(H-3,C-14,54Mn,58Co), still can't be found even many efforts were taken. The related reactions...
  34. mhsd91

    Particle Phys.; Isospin conservation for cross sections of scattering

    Homework Statement What relations can you derive from isospin conservation for the cross sections of the following scattering processes: K^{+} + p → K^{+} + p K^{+} + n → K^{0} + p K^{0} + n → K^{0} + n The Attempt at a Solution I do not really have my own solution as I've...
  35. Q

    Partial wave scattering cross section in spherical well

    Homework Statement Consider the spherical well such that V(r<a) = -V0 and V(r≥a) = 0. Calculate the l = 0 partial wave scattering cross section in the low energy limit for this potential. Homework Equations σ = \frac{4 \pi}{k^2} * \Sigma (2l+1)*sin^2(\delta_l) The Attempt at a...
  36. C

    Octagonal Cross Section with Parabolically Increasing Span

    Octagonal Cross Section with Parabolically Increasing "Span" Hi all, could some one tell me what I am doing wrong in my analysis in the attached file? Its a parabolical flare column with an octagonal cross section. The effect of the parabolic flare simply stretches the octagon so that the...
  37. Z

    Cross Product of Two Vectors - Mag. 2 & 4

    One vector with mag 2 pointing East. Other one is mag 4 pointing 30° west of North Would you use sin or cos and would it be - or + I did (2*4)cos60°=+4 because they're vectors and we have the A/H sides. I'm worried about that though because we may use sin? Also Cos is (-) in...
  38. C

    Area of a tunnel with two functions creating the cross section

    Homework Statement Two curves/functions make up one side of a tunnel (the tunnel is symmetrical, so the other side is the same) Function 1: y = 5 + (2/((x-4)^3)) Function 2: y = (x -1)^3 - 5 I need to find the area of the tunnel, so I can find the amount of dirt that needs to be removed...
  39. F

    Cross product in cylindrical coordinates

    In my physics textbook we have d\vec{l}=\hat{z}dz and then it says d\vec{l}\times \hat{R}=\hat{\phi}\sin \left (\theta \right )dz How so? What is \hat{z}\times\hat{R}? If it is \hat{\phi} then where does the sine come from?
  40. P

    How Does Polarization Affect Electromagnetic Wave Scattering by a Free Electron?

    Homework Statement A plane monochromatic electromagnetic wave (polarized in x-direction and propagating in the z direction) is scattered by a free electron initially at rest. Homework Equations \vec{E}=E_0 \exp(i(kz-wt)) \hat{x} \vec{B}=\frac{E_0}{c} \exp(i(kz-wt)) \hat{y} The...
  41. F

    Why Does the Cross Product Give a Different Direction Than Expected?

    I am trying to compute -dx i CROSS -x i -y j i,j,k are the unit vectors x is from -∞ to ∞ and y can only be negative. Right hand rule tells me that the cross should be in the negative k direction but computing the cross product gives me y dx k. What's wrong?
  42. X

    Solutions to cross product, a x u = b

    Studying outer product spaces at the moment and thought I'd quickly recap on the cross product when I stumbled across this problem which has me fairly stumped! If a,b∈R^3 with a≠0 show that the equation a x u = b has a solution if and only if a.b = 0 and fi nd all the solutions in this case...
  43. J

    Cross Sectional Area, Stress and Strain confusion

    Homework Statement For each material calculate the cross sectional area in m². Each sample is of rectangular cross section 20mm by 1mm. Produce Stress and Strain tables for the data. TEST DATA FOR X (N) EXTENSION (mm) 1000 0.48 2000 0.60 3000 0.70 4000 0.80 Homework...
  44. L

    What Is a Crosspoint Switch in Electronics?

    Does a criss-cross resistor network exist? I need something (preferably passive), that comes in both criss cross and straight paths. Maybe a switching array of some sort? I am looking for something that connects- A-->A B-->B C-->C D-->D and A-->D B-->C C-->B D-->A It can be...
  45. B

    QFT: differential cross section from center of mass to lab frame

    I have the following process: two ingoing particles, a photon hitting a nucleus, and two outgoing particles, the nucleus and a pion. I have computed |M|2 and the differential cross section in the center of mass frame dσ/dΩCM; I now have to go into the lab frame, where the nucleus is initially at...
  46. W

    Amount of scattering calculated from scattering cross section

    I was reading Wikipedia article on Rayleigh scattering and came upon this: "...the major constituent of the atmosphere, nitrogen, has a Rayleigh cross section of 5.1×10^(−31) m^2 at a wavelength of 532 nm (green light). This means that at atmospheric pressure, about a fraction 10^(−5) of...
  47. S

    Divergence of a cross product help

    I need to prove the identity: \nabla(\vec{A} \times \vec{B})=\vec{B} \bullet(\nabla \times \vec{A}) - \vec{A} \bullet( \nabla \times \vec{B}) I need to prove for an arbitrary coordinate system, meaning I have scaling factors. The proof should be quite straight forward if you use the levi...
  48. B

    Which wood cross section can carry highest uniform load

    Which wood cross sectioπ caπ carry hïghest uπiform load Homework Statement Homework Equations Moment of inertia for rectangle I=(1/12)bh3 τ=(VQ)/(I*b) σ=(MV)/I The Attempt at a Solution I started by finding reactions at B and C Then drew the sheer and moment diagrams (to save...
  49. A

    Cross Products Verifying Third Vector Orthoginality?

    I have a question. Let's say you have three distinct, non zero vectors that lie in the same plane. Can I verify the othoginality of the third vector using strictly cross products? I know I can just do the dot product and if it equals to 0 then its orthoginal to the plane; however, I came across...
  50. J

    Why is the cross product perpendicular?

    Why is the cross product of two vectors perpendicular to the plane the two vectors lie on? I am aware that you can prove this by showing that: (\vec{a}\times\vec{b})\cdot\vec{a} = (\vec{a}\times\vec{b})\cdot\vec{b} = 0 Surely it was not defined as this and worked backwards though. I...
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