Cross Definition and 1000 Threads

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...

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 I am trying to submit for publication: [Reference to unpublished paper deleted]

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...

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

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})...

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

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...

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...

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...

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...

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...

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...

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 ...

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...

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

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...

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...

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?

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...

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...

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...

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...

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!

What is the difference between a hybrid and a crossbreed?

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}/...

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...

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...

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

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...

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>...

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...

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...

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...

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##...

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...

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...

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 +...

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...

Homework Statement [/B] To cross a river with a current (flowing downstream) in the least amount of time, a boat should point a) directly at the opposite shore b) somewhat upstream c) somewhat downstream d) in a direction that will take the boat directly across e) downstreamHomework...

Hello, I have been poring over this problem for days, and I would really appreciate some help. I'm not sure if it's an algebra problem exactly. It's from my physiology class. The professor said it's simple cross multiplication, and I asked him to explain it again, but I didn't understand his...

Hello everyone. I have been practicing for my exam in fiber optics, and stumbled upon the following question: We have a transmission system with 3 channels, composed of a single mode fiber and a dispersion compensation fiber. Specifications are given for each. We need to calculate the channel's...

Hi - from orbital angular momentum components, $[L_x, L_y] = iL_z$ My book claims 'Hence, $ \vec{L} \times \vec{L} = i\vec{L} $' I'm keen to know how they get that, an also why that cross products isn't = 0, like $A \times A$ would be ?

I got to here in a simple exercise (orb. ang. momentum cords), realized I was applying something I didn't understand ... $L = -i \begin{vmatrix}\hat{x}&\hat{y}&\hat{z}\\x&y&z\\\pd{}{x}&\pd{}{y}&\pd{}{z}\end{vmatrix}$ I 'know' it equates to $L_x =-i \left( y\pd{}{z} - z\pd{}{y} \right) $ - but...

Homework Statement The problem asks me to find \frac{d\sigma}{dz} for u\bar{u} \rightarrow t\bar{t} via the strong interaction and then to find the total cross section via QCD. I'm wondering what the difference is? I was just going to write the feynman rules for QCD to get the amplitude and...

Homework Statement Angular momentum is the cross product of r and mv. But why is there mvR outside of the paranthesis? And where did the v go in the second paranthesis - shouldn't the second paranthesis be (-v*sin(ωt), v* cos(ωt)). Does anyone have any idea how they did the cross product...

Hi folks, I'm working on Fluka nowadays which you can found from here if you are not familiar. It's a very useful and widely used Monte Carlo simulation package. My main goal is to be able to perform total cross section calculation with it. So far, please consider I'm a rookie, I've done some...

Lets look at the force on a wire segment in a uniform magnetic field F = I∫(dl×B) I am curious if, from this, we can say: F = I [ (∫dl) × B] since B is constant in magnitude and direction

A method for finding the shortest distance between 2 skew, non intersecting lines is to 1st find the common normal, using $ \vec{n} = \frac{\vec{v_1} \times \vec{v_2}}{|\vec{v_1} \times \vec{v_2}|} $ I'm looking for a proof or intuition as to why this is true please? Then apparently we get the...

So my question is simple. If the current doesn't change sign, is it considered AC or DC? I seem to recall we called it DC when I briefly saw it. However after a quick google search I'm confused. Some said that for example an AC signal offset with a DC signal to show this behaviour should be...

Homework Statement See pictures. There are 2 parts to the problem but I can probably figure out the second part once I get the first part. [/B] Homework Equations Antinodes (minimum pressure) at Nodes (maximum pressure) at [/B] Equation for a standing wave: The Attempt at a Solution...