Cross Definition and 1000 Threads

Hello all, I have a fellow grad student who is convinced that the differential cross section: \frac{d\sigma}{d\Omega} is truly a ratio of differentials. That is you have an infinitesimal cross section divided by an infinitesimal solid angle. I contend that when we write...

Three forces with magnitudes F_a, F_b, F_c act on a point mass, pulling in unit directions a, b, c, respectively. Thr forces are in 'equilibrium' which means that F_aa + F_bb + F_cc = 0 By taking the cross product with a, show that F_b(a \times b) = F_c(c \times a) and find two similar...

Hello, I am new here and I am very happy to find a webpage like this. It has been 6 years sice I graduated from Physics and I haven't dealt with derivatives of vectors for a long time. Recently I have been accepted for the master degree and trying to built my memory again. My homework...

hi, I'm currently doing a mechanics module at Uni. The thing is, I'm not very sure about rules regarding the vector cross product and dot product. For example, it says in my notes for angular momentum: "Introducing polar coordinates \mathbf{r} = r(cos \Phi \mathbf{i} + sin \Phi...

Calculating Surface area/volume from 2D cross section?? I'm feeling a little stupid today and I need some help...:-p Assume that I have a radially-symmetric 3D object (for example a candle stick or the base of a table lamp) and that I can calculate the surface area of the largest longitudinal...

I have learned just about the right hand rule in vector cross product. How is this proved? Can anybody give an example where the cross product plays an important role and where the vector cross product formula is obeyed? Our professor just told us that the torque due to a force acting on a body...

I have a two-part problem. The first part gve me a position vector r and a Force vector F acting upon r and I needed to find the magnitude of the torque about the origin. I took rxF and got the correct answer. Part two asks me to find the torque about the a new point (a,b). So instead of r...

Hey, I have the following question, Simplify (au + bv) x (cu + dv) where a,b,c,d are scalars and u,v are vectors. I know that we can take ab ab and cd outside to make the expression ab(u +v) x cd(u + v) but I am unsure on where to go from here. Thanks in advance

What is "momentum transfer cross section" ? Hi all, I'm reading a book on electron-molecule interactions and I'm puzzled by a quantity (well, by the difference in definition of two quantities). The book is, for your information, "fundamental electron interactions with plasma processing gases"...

A figure contains five equal squares in the form of a cross. Can you show how to divide this figure into four equal parts which will fit together to form a square

Hello everyone, this should be a simple problem..its for matrices and I already delt with this in calc III and physics but it says: find a unit vector with positive first coordinate orthogonal to both a and b. a = <1,2,1> b = < 1,8,1> so i took the cross product and got: <-6,0,6> it...

This is the question I have from my book, I have tried numerous methods of solving it, but I cannot obtain the correct answers. If someone could get me started with an equation I could go from there... Jane, whose mass is 50kg, needs to swing across a river (having width D) filled with man...

I got the first part of this question but can't seem to get the 2nd part.. A 105 V potential difference is applied to a space heater that dissipates 1000 W during operation. (a) What is its resistance during operation? 11.025 OHM (b) At what rate do electrons flow through any...

I have two vectors A = 2x + 3y - 4z and B = -6x - 4y + z. The problem asks me to find the component of A X B along the direction of C = x - y + z. So I did put A and B into a matrix, but I didn't get the correct answer, which is -14.4. What am I doing wrong?

Hello everyone, I'm stuck on trying to prove the cross product rule for derivatives. I Have to add the right terms and its suppose to be easy but that's what i can't figure out! any help would be great! here is what I have: http://img135.imageshack.us/img135/5540/opopo3ej.jpg

Does anyone know where I can find the derivation of the cross product. I know how to use it and the like but I do not understand why the norm of the matrix : \left[ \begin{array}{ccc}i & j & k \\n1 & n2 & n3 \\m1 & m2 & m3 \\\end{array}\right] yields the vector perpendicular to 'n' and 'm'.

11. Calculate the area of the parallelogram having the vertices (1,2,3),(4,-2,1),(-3,1,0), and (0,-3,-2). To solve this problem I need to find two vectors that share a common point? Then I can take the magnitude of the cross product of those two vectors to find the area of the...

I have read about "Thompson Cross section for free electrons" My problem is there must be the other cross sections photons are scattered by free electrons. photons must be scattered by aka protons and as well by alpha particles. Is there any defined cross sctions for the other particles as...

Question answered! Thanks!

I am having trouble setting this problem up. The problem says: Find a vector N that is perpendicular to the plane determined by the points P(0,1,0), Q(-1,1,2), R(2,1,-1), and find the area of triangle PQR. I know that the cross product of two vectors is perpendicular to the plane of a and b...

Runner A is initially 4.54 mi West of a flagpole and is running with a constant velocity of 7.06 mi/h due East. Runner B is initially 4.34 mi East of the flagpole and is running with a constant velocity of 6.82 mi/h due West. Consider East to be in the positive direction. What is the...

In the book "Gauge Theories of the strong, weak, and electromagnetic interactions" by Chris Quigg the calculus of the scattering of proton-electron is esbosed (chapter 7, section 3 , pag 168). He get the result (in the lab frame): \frac{\mbox d^2\sigma}{\mbox d E^\prime\mbox...

Does anybody know where to get the expected cross section for Z at the LHC (pp at 14 TeV)? (it would be great if you could provide a reference).

Hey guys, Can you help me out with this one. I want to prove the that the cross product |A||B| sin( \theta) is equal to its components, =<a_2b_3-a_3b_2,a_3b_1-a_1b_3,a_1b_2-a_2b_1> . A thing I find Annoying is that most books just say, we define the dot product in component form as ""...

i need help with the following: note that the big dots represents the dot product 1. suppose that a \bullet b = c \bullet b for all vectors \overrightarrow{b} . show that \overrightarrow{a} = \overrightarrow{c} . i suppose i can't simply divide out the b, right? anyway, i tried...

a crate is sliding (disregard friction) with d=(-3.0 m)i while a steady wind pushes against the crate F=(2.0 N)i + (-6.0 N)j How much work is done by the wind on the crate? Ok W=Fd so I want to multiply the two vectors together. [(-3.0 N)i ]*[(2.0 N)i + (-6.0 N)j ] Do I use a cross...

Why does torque, magnetic fields and others, work with something like the vectorial cross product? A plane director vector of intensity equal to the area of the paralelogram formed by the other two? Anyone? Basic Statistics Physics? Thank you all in advance.

When using cartesian coordinates, I use the following expressions to calculate the cross product of the basis vectors: i \times j = k j \times k = i k \times i = j j \times i = -k k \times j = -i i \times k = -j Can I do the same in polar coordinates? How could I write the cross...

Simple question: is the cross product defined in R^n ? In my linear algebra textbook, they talk about the dot product in length but don't even mention the cross product.

"The area of a parallelogram spanned by two vectors, v1 and v2, is ||v1 X v2||." Would someone help me understand why this is true?

How do you go about crossing two vectors if they are in cylindrical coordinates? I have one vector in the direction of R and another in the direction of theta. Can this be done?

find the cross product a x b of the vectors a = 5.0m,i and b=4.3m,k 5.0m\ast 4.3m\ast \sin (90)=22m^2,\hat {j} The back of the book gives -(22m^2)\hat {j} Where does the minus sign come from?

In this problem, you will estimate the cross section for an earth-asteroid collision. In all that follows, assume that the Earth is fixed in space and that the radius of the asteroid is much less than the radius R of the earth. The mass of the Earth is M_e, and the mass of the asteroid is m. Use...

I'm going through my intro to mechanical engineering material and there was one thing I was never clear on: If you have a cross section of a rod, why isn't its' area at a cross section pi * r^2 as a opposed to piD^2/4, where D is the diameter?

Ok here's the situation: 2 Soldiers are just standing around. They pretty much have standard clothing and equpiment on and a normal helmet. About 20 kids run up to them and from about 20 yards away, start hurling fist sized rocks at them. The soldiers respond by first firing a 40mm riot...

I desperately need help, for I am quite lost on this question: Consider the example of a positive charge moving in the xy plane with velocity v = cos(theta)x + sin(theta)y (i.e., at angle theta with respect to the x axis). If the local magnetic field is in the +z direction, what is the...

I'm not even sure such a thing exists :P. Anyway, if it does, is it correct that it is: Xc = -Y Yc = X (rotation 90 deg counter clockwise) Couldn't find anything about it on google...

I do not understand something about cross products. Say, \vec A\times \vec B=\vec C=(C_x, C_y, C_z) and, \vec C=(A_x \hat x+A_y \hat y+A_z \hat z)\times (B_x \hat x+B_y \hat y+B_z \hat z) but why is this equivalent to (A_x B_y - A_y B_x)\hat x \times \hat y + (A_x B_z - A_z...

Although, the dot product works in infitine dimensions, it is not the case for the cross product. Anybody know in what dimensions the cross product can be defined?

using Darcys law... ...what is Cross sectional area of cylinder?

Is there any neat way/rule to write: \vec B \times (\vec \nabla \times \vec A) ? I've tried it myself and found (e.g) for the x-component: \left(B_x\frac{\partial A_x}{\partial x}+B_y\frac{\partial A_y}{\partial x}+B_z\frac{\partial A_z}{\partial x}\right)-\left(B_x\frac{\partial...

Is anyone familiar with Breit-Wigner Cross section? Say, for a reaction with 2 particles in the initial state, 1 intermediate and 2 final: \sigma = \frac{g \pi \lambda^2 \Gamma_i \Gamma_f}{(E-E_0)^2 + \frac{\Gamma^2}{4}} I can't see why for the wavelength we should use the momentum of...

I'm looking either for online resources or reference to a good book. I've been trying to help someone with a homework problem in a course entitled, Elements of Mechanical Design which uses Mechanical Design of Machine Elements and Machines by Jack A. Collins. The book sucks. The system...

The base od a solid is a region in the 1st quadrant bounded by the x-axis, y-axis and the line x+2y=8. If cross sections of the solidperpendicular to the x-axis are semicircles, what is the volume of the solid? How come the answer isn't just the intgegral from 0-8 of 1/2pi(4-x/2)^2

What is meant by Copolarization and Cross polarization? How does EM wave travel in such polarizations?

What is the differential cross section for photo-electric effect? Is there a paper that explains this in more detail? Thanks in advance for any responses!

The textbook says, "The cross section, \sigma , is the transition or reaction rate per scatterer in the target, per unit incident flux". It gives the formula \sigma = transition \ rate \cdot \frac{1}{\# \ of \ scatterers \ in \ target} \cdot \frac{1}{unit \ incident \ flux} =...

In the problem: A horizontal boom supporting the sign is of uniform construction and weighs 50 N. If the sign weighs 150 N, the tension in the supporting cable is? Could I use the cross product and if so how? The answer is 350 N.

if jon rows a boat at 4m/s the river is moving at 6m/s and the river is 300m how long does it take to row across. I need the equation

Force F = (4.0 N) i + (-2.0 N) k acts on a pebble with position vector r = (2.50 m) j + (-1.3 m) k, relative to the origin What is the resulting torque acting on the pebble about a point with coordinates (2.0 m, 3.0 m, 2.0 m)? Ok so I just completely forgot how to work with vectors when...