Cross Definition and 1000 Threads

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...

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...

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...

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...

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...

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...

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...

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...

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?

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...

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?

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...

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...

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...

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...

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...

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...

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...

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...

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...

Homework Statement If a, b, c, d are all vectors contained in the same plane, explain why (a X b) X (c X d) = <0,0,0>Homework Equations The Cross Product! The Attempt at a Solution I know that since all of the vectors are in the same plane that means that a cross product between any of the...

Hello, This query isn't concerned with solving a problem, but only with details appendant to the problem. The question is as follows: A uniformly charged ring of radius 10.0 cm has a total charge of 64.0 µC. Find the electric field on the axis of the ring at the following distances from...

Okay, now that my question has been cleared up, what is the cross product of a constant vector and a vector? Is there a formula?

What is the cross product of a constant and a vector? I know that the cross product between two vectors is the area of the parallelogram those two vectors form. My intuition tells me that since a constant is not a vector, it would only be multiplying with a vector when in a cross product with...

By using both cross and dot products, the angle between 2 vectors can be found. But there is 1 question that I tried for countless times that the result of cross product and dot product are not the same. Here is the vectors that I am talking about A= 2i+3j=k B= -4i+2j-k The result by...

Hello! I´m confused about this concept.. It seems rather trivial, but my teacher is not that pedagogical and describes it as a rather diffcult concept so maybe I misunderstood it. Given the definition in Sakurai and the scattering of only one particle it seem to be a kind of "denisty" per...

I'm taking multivariate calculus and my teacher just introduced the concept of cross products a week ago. Reading the Wikipedia page, I see that cross products only work in three and seven dimensions, which is puzzling. One use of the cross product for our class is to find the vector...

First question: a x b = -b x a Why is this so? As I understand, a major purpose of the cross product (if not, the purpose) is to find a third vector that is perpendicular to two other vectors simultaneously. Let's say a x b = c. Shouldn't the answer really be, a x b = +/- c? Since, of...

$$ \frac{d}{dt}[\mathbf{a}\cdot (\mathbf{v}\times\mathbf{r})] = \dot{\mathbf{a}}\cdot (\mathbf{v}\times\mathbf{r}). $$ How is this true? Shouldn't the derivative affect the cross product as well?

Hi I need to plot the (differential) Rutherford cross section as a function of the scattering angle in the CM frame. the reaction is a typical projectile on stationary target. I know the projectile energy in the lab, θcm and the masses. I am confused over which energy to use though. I know...

If e1 and e2 are vectors in ℝ3 show that e1 x e2 = e3, e2 x e3 = e1 and e3 x e1 = e2. I have tried to prove this but I can't get it. My attempt: Step 1: [a1, a2, a3] x [b1, b2, b3] = [a2b3-a3b2, a3b1-a1b3, a1b2-a2b1] Step 2: [b1, b2, b3] x [a2b3-b2a3, a3b1-a1b3, a1b2-a2b1] =...

I'm a bit confused by something Peskin & Schroeder say about differential cross sections. In my printing, this is on page 101 in the paragraph preceding the one that contains eq. 4.62: "In the simplest case, where there are only two final-state particles, this leaves only two unconstrained...

Hello! We are trying to verify if an acoustic standing wave has been established in a cavity. In order to do so, we are giving a constant frequency signal to a speaker. We are picking up the signal at two locations, one very close to the speaker(reference signal) and at a particular...

Homework Statement From John Taylor's Classical Mechanics: Show that definition (1.9) of the cross product is equivalent to the elementary deinition that R x S is perpendicular to both R and S, with magnitude rssinθ and direction given by the right hand rule. [Hint: It is a fact (though...

Lagrangian I have is little bit massy so I don't write in here. Like in ψψ(dagger) , or ψ∅ -> ψ∅, How can I calculate the differential cross section or total, or amplitudes?

Hey everyone! I have the following question for you guys to settle an argument: If you were an inhabitant of Flatland and a cube decided to visit you like the sphere did, would you be able to see more than 2 sides at a time? My answer is no because Mr. Cube could appear as a point, a square...

A=$\begin{bmatrix}1\\1\\0\end{bmatrix}$, B=$\begin{bmatrix}3\\1\\-1\end{bmatrix}$ C=$\begin{bmatrix}5\\3\\-1\end{bmatrix}$, D=$\begin{bmatrix}4\\0\\-2\end{bmatrix}$ Find the coordinates of a point E such that A,B,C,E forms a harmonic range. This means that the cross ratio is -1.

Homework Statement abstract question, but we can assume the volume,V to be filled is 0.0001m3 and time for it to filled up water is 60seconds, water density is 1000kg/m3, so how much should be the cross sectional area,A for the tube?Homework Equations Volume flow rate=delta Volume/delta time...

I'm learning scattering theory from Griffiths' book, and I don't really understand the meaning of differential cross section; it's one of those things that I find hard to conceptualize and give a physical meaning to. The most intuitive description he gives is "the proportionality factor between...

Homework Statement A 1.47kg particle moves in the xy plane with a velocity of v = (4.59i - 3.28j)m/s. Determine the magnitude of the particle's angular momentum when its position vector is r = (1.35i + 2.57j)m. Homework Equations p = mv L = r x p (the x is supposed to be a cross...

Hello, I've found in some of the articles on experimental quantum physics the term "Topological cross section" Now I'm trying to understand what is it and in particular what the difference between topological and differential cross section? Thanks in advance for suggestions on any reading...

Homework Statement A lever is orientated along the y direction in a Cartesian coordinate system. The length of the lever is 0.5m and one end of it is at the origin of the coordinate system. A (3i-5j)N force applied to the other end of the lever. Calculate the Torque produced by the force...

trig functions cross multiplying?? Homework Statement sinx/cosx - 2sinxcosx/1Homework Equations none??The Attempt at a Solution when I cross multiply, should it be sinx-2sinxcosx/cosx or sinx-2sinxcos^2x/cosx ?? here's a pic: http://tinypic.com/r/24fgvmv/6

1. Homework Statement Two vectors are given by A = -6 i + 5 j and B = 1 i + 4 j Find A X B (answer only in terms of i, j, k) Find the angle between A and B (answer is terms of degrees) 2. Homework Equations All I was told was that if I set a 3x3 matrix like this: i j k -6 5 0 1 4 0...

Homework Statement Two vectors are given by A = -6 i + 5 j and B = 1 i + 4 j Find A X B (answer only in terms of i, j, k) Find the angle between A and B (answer is terms of degrees) Homework Equations All I was told was that if I set a 3x3 matrix like this: i j k -6 5 0 1...

A 7.50kg block slides down a frictionless ramp of height 2.25m at a velocity of 1.50 m/s. it crosses a rough patch that is 2.5m long and exerts a force of 3N. It then continues to the other side of the ramp which is angled at 35 degrees(I don't think this matters b/c it is frictionless). How can...

qq- --->qq- differential cross section and mandelstam variables Homework Statement for the problem statement please look the attachement Homework Equations The problem is asking to express the mandelstam variables in temrs of the scattering angle θ.I would like to ask the quastion...

Hi, I'm reading an article called SuperSymmetric Dark Matter, by G. Jungman et al. doi:10.1016/0370-1573(95)00058-5 and in section 3.2, he claims that <σv> ≈ \alpha^{2}(100 GeV)^{-2} \approx10^{-25} cm^{3} s^{-1},[\itex] for \alpha \approx \frac{1}{100}. When I run through the calculation...

Homework Statement Here is the problem: I have to calculate the maximum stress for A, B and C. Homework Equations I used: σ = y*F*L / 4*I (but I don't think this is right) σ = maximum stress y = Perpendicular distance from to neutral axis F = load L = length of beam I...

I have asked for help from a math professor and it didn't really help. It would be absolutely fantastic if one of you could help me out. Here is the problem verbatim. A trough has a trapezoidal cross section with a height of 1 m and horizontal sides of width 0.5 m and 1 m. Assume the length of...