Cross Definition and 1000 Threads

If a system is made up by two subsystems, for example, the atom and the photon. and let's assume the state of the atoms is described by |\phi\rangle, while the state of the photons can be described by |n\rangle, The Kronecker product of the |\phi\rangle and |n\rangle can be used to describe the...

As we know RCS is measure of how detectable an object is with a radar. But I don't understand one thing. If we take a sphere as an example, we can see that RCS is the largest in forward direction (forward scattering). If the sphere is to big (radius>>lambda), still this forward scattering is...

So in our notes we are given a general quadratic equation in three dimensions of the form: Ax^2 + By^2 + Cz^2 + Dxy + Eyz + Fxz + Gx + Hy + Iz + J = 0 And then they say, by some rotation we can change this to the standard form: Ax^2 + By^2 + Cz^2 + J = 0 The lecturer said don't worry...

What are three different ways that i can produce a hole with a square cross section in a plate with a thickness of at least 1"?

Hi, I'm doing a project to see the feasibility of transmuting tungsten into platinum on a small scale (maximum output of 1 kg per month). However, some of the cross section data that I need seems to be hard to find. Now because I am new to this, I don't know if its because no body has...

Hi all, I think that the off shell decay dosn't decrease the decay cross section, I mean if a particle X decays into a jet pair has mass for example Mjj ~ 130 GeV, being X has mass M ~ 130 GeV so decay in resonance or on shell into jj or being MX even much greater ~ 2000 GeV , this...

Hi all I was trying to understand the Born-Bethe approximation related to cross sections for atomic and molecular collisions. All the stuffs that i got are explaining in complicated way which am not able to follow. Can anyone explain in simple terms what the theory explains? It will be of...

Cross product is used to find the perpendicular vector of two vectors. If there is any two vectors in a plane then there is always a perpendicular vector to both of them. So in circular motion if the motion is horizontal then is there a perpendicular force to the object in circular motion?

Vectors -- dot product and cross product? Hello may i know when to dot product and cross product?? both look to same to me..

Homework Statement Using the Eikonal approximation (1) Determine the expression for the total scattering cross section of a particle in a potential V(r) (2) Using this result, compute the total scattered cross section for the following potential. V(r)= \begin{cases} V_0, \text{for } r < a \\...

I am trying to understand the difference from a physical phenomena point of view, not just math. Surprisingly I think I got the cross product like in rotational momentum. You have the momentum vector and we have effective distance from the momentum vector R that needs to be perpendicular to the...

What does "cross section area" mean when dealing with stress/strain? Homework Statement For clarification, here is an example problem: A circular steel wire 2 m long must stretch no more than 0.25 cm when a tensile force of 400 N is applied to each end of the wire. What minimum diameter is...

If u × v = u × w, so v = w ?

Hi, I am self-teaching Quantum Elctrodynamics, and have come across something which I do not understand. I would appreciate feedback from anyone on this specific issue from Atchison & Hey, "Guage Theories in Particle Physics" pg 238-239: In calculating the u-channel electron-muon...

I'm designing a cross yagi as one component of a capstone project. The design I have right now is 3 elements per polarization, counting driven elements (total of 6 elements). I ran a quick 4nec2 simulation of a single polarization (3 elements) using center excitation on the driven element and...

I've always heard that the cross product only exists in a well defined way for 3 and 7 dimensions. From my own reading I've found that a cross product in 3 dimensions is nothing more than the product of two quaternions with only pure imaginary components (that is, the real part is zero)...

Homework Statement For a laser, assume single mode operation, only lifetime broadening due to A21 and A1. Write out the rate equations for the atomic densitions N1 and N2 and the flux \Phi. Then there's a diagram where there's 2 stats. Pump rate is P, stimulated emission between 1 and 2 is...

Hi all, I'm trying to work out how I can get the set at specific index in a cross product without creating the whole product. For instance: I have array A of length 512 I also have a number that specifies how many times that array needs to be 'cross-producted' against itself. This gives me...

I understand that the cross product, in lay mans terms doesn't exist unless we're in 3 dimensions. When you multiply two matrices together I have been told you get something similar. I hear that this is because a matrix can be treated as a vector. So if we are talking about measurable...

I am a bit confused often when I have to compute cross products in other coordinate systems (non-Cartesian), I can't seem to find any tables for cross products such as "phi X rho." in spherical I think that these unit vectors are considered to be "perpendicular," so would phi X rho just be "+/-...

Homework Statement Ok, so in a lab I was preforming Izod impact tests on notched polymer specimens. To complete my calculations I need to determine the correct cross-sectional area to use (Which is baffling me as the simple things usually do) The sample was loaded with the notch facing...

Homework Statement Given two vectors A⃗ = 4i + 7j and B⃗ = 5i − 2j , find the vector product A⃗ × B⃗ (expressed in unit vectors). Express your answer in terms of the unit vectors i, j, and k. Homework Equations The Attempt at a Solution I know how to cross and multiply them...

Homework Statement Two stones are thrown simultaneously, one straight upward from the base of a cliff and the other straight downward from the top of the cliff. The height of the cliff is 6.69 m. The stones are thrown with the same speed of 9.97 m/s. After what time do the stones cross paths...

Hi everyone, What does \int \vec{f} × \vec{dl} mean? does it mean "The Line Integral of Vector Function on a positive curve L"? And are the following named correctly? \int \vec{f} . dl : Scalar Line Integral of a Vector Function \int udl : Line Integral of a Scalar Function

Hi; I've been trying to solve the problem myself but i really don't what could be wrong; The problem says : Make the change of variables x=ucos−vsin y=usin+vcos where the angle 0<(phi)<2 is chosen in order to eliminate the cross product term in x^2+xy+y^2=6 Then find the standard form of...

Dear Forum ： I'm looking for proton-proton inelastic cross section in MeV. There are lots of results in GeV, TeV. But I can not find the results in MeV in ENDF nor TENDL. https://www-nds.iaea.org/exfor/endf.htm ftp://ftp.nrg.eu/pub/www/talys/tendl2011/proton_html/proton.html Please advise...

Homework Statement The value of 3i(dot)(jxk) Homework Equations The Attempt at a Solution I know the answer is 3, but could someone please explain how to work this problem?

I know that for the tangent unit vector ##t##, normal unit vector ##n##, and binormal unit vector ##b## that ##b=t\times n## and ##n=b\times t##. Is it true that ##t=n\times b##? **Edit** Ah! Yes it is. Nevermind. I should have known this was true.

I was developing a pythagorean theorem proof based on the cross product of two vectors..Below is my final solution...My problem is I had to get around using the distance/magnitude formula because that is using the pythagorean theorem to prove the pythagorean theorem. But after searching, it may...

Homework Statement See the problem attached in this post. Homework Equations See the problem attached in this post. The Attempt at a Solution I set my limits of integration with respect to z axis and got an upper limit of 2 since that's the vertex point/height of the pyramid...

While I was going through my course material of Aldehydes and Ketones, I came across Cannizzaro Reaction. It is of 3 types, namely: Self Cannizzaro, Cross Cannizzaro and Intramolecular Cannizzaro. I understood the Self one but was unable to understand the other two. In the Cross one,why is...

Homework Statement In 1993 the radius of Hurricane Emily was about 350 km. The wind speed near the center ("eye") of the hurricane, whose radius was about 30 km, reached about 200 km/h. As air swirled in from the rim of the hurricane toward the eye, its angular momentum remained roughly...

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...

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...

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?

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...

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?

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...

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...

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...

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...

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...

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...

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...

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}...

can you show me derive cross product from dot product?

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

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} = ?

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...

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...