Cross Definition and 1000 Threads

Homework Statement So I have several problems on my homework which deal with the application of cross product and its magnitude to find areas. I know how to do cross product, and I know how to find the magnitude, however, no matter how many times I try to calculate it, I get the wrong...

Homework Statement The two vectors a and b lie in the xy plane and make angles α and β with the x axis. a)By evaluating a • b in two ways (Namely a •b = abcos(θ) and a • b = a1b1+a2b2) prove the well-known trig identity cos(α-β)=cos(α)cos(β)+sin(α)sin(β) b)By similarly evaluating...

'Ello, I have a question regarding the results in this paper (and another which I will mention later) http://arxiv.org/abs/hep-ph/0212199 Now, I'm not so concerned about the 'braney' bit, but more their definition of the cross section in Eqn. (46). They have included the usual (2j+1)...

I have two problems: Homework Statement In general, what can be said about the vector product x×(x×y) The Attempt at a Solution I thought the result of this would be parallel to y. However the answer suggests it is orthogonal to x. Can anyone explain how I could approach this...

I was doing a question in a test involving the system of moments , you are given 2 force vectors and two points respectively . And you must find a third point and force to make the 3 moments in equilibrium . So I did the cross product with the first force vector and its point and then with the...

Hello, currently I work on 2->3 scattering process. So there exist five external momenta and in my case 5 different Feynman diagrams, for which I have already calculated the full matrix element. The matrix element is a function of various scalar products of the four-momenta. This scattering...

Homework Statement Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Homework Equations y = x^2, x = y^2 about y = -1 The Attempt at a Solution I tried using both cylindrical and washer methods - but for...

Homework Statement Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Homework Equations y = \sqrt{x-1} , y = 0, x = 5; about y = 3 The Attempt at a Solution I already completed graphing it, but not really sure how...

Suppose that we have a cross-product of vectors. a × b = c Now suppose that we have an orthogonal matrix M. Is it true that (M a) × (M b) = M c ? My intuition is that here we are moving to another coordinate system and performing a cross product in this new system. I can't find an...

Basically, we have to prove that A X B is equal to ABsinθ Now a crucial step towards the proof is proving that (AXB).(AXB) is equal to (AB)2 - (A.B)2 After that it is fairly simple. But unfortunately, I can not prove the identity. I've tried expanding it into components but things are...

Homework Statement A beam has a solid square cross section of 100mm and is simply supported by two supports 3m apart. Calculate the dead load that can be safely supported when applied to the middle of the beam. Homework Equations Solid square cross section of beam: 100mm Material...

the higher the energy of the photon, the more powerful it can ionize an atom but why then the absorption cross section decreases with the photon energy?

Hello, I'm not sure if this is the right section because this is somewhat of a hybrid of math and physics. Say I have a ball in 3D space, its initial position and its' initial acceleration. Furthermore I have another point in 3D space which I want the ball to pass through, if possible. The...

a basic problem but i have no idea how to measure it

A cross B equals zero is a test for orthogonal cases. If AxB=0 then A is perpendicular to B.

Hello. I was hoping someone could help me understand some units. In several papers, I have seen the two photon LIF signal written as: S = n*(Ω/4π)*T*G*σ*(E/hv)^2*η*a where the units are n (density of measured atom): #/cm3 Ω/4π (solid angle fraction): unitless T (optical transmission...

Homework Statement A dot B=0.707m^2, A cross B=4.950m^2 k^. If |A|=2.500m and B makes an angle of 135° with the positive x-axis, what are A and B in component form? Homework Equations A*B = |A||B|cos(θ) A X B = |A||B|sin(θ)@RHR The Attempt at a Solution I have no prior physics...

How do particle scattering cross sections scale with energy in colliders? Particularly photons, electrons, protons, and gold or lead nucleii? (If necessary, break this into four separate questions.) It is stated that due to the Heisenberg uncertainty principle, it takes more energy to...

While we calculate cross product of two vectors let A and B we write ABsinθ. And while we calculate dot product of them we write ABcosθ. Why particularly we use sinθ for cross product and cosθ for dot product.Is there any physical reason why we choose sine for cross product and cosine for...

OK, I realize I am probably on a hiding to nothing here, but please bear with me for now, I have tested my calculations so carefully that I am totally convinced that I have found an error in two published accounts of the BL line element . . . The first is Visser, equation (57)...

Homework Statement The area is bounded by the equation y=x^2, x-axis and the line x=3 and is perpendicular to the x axis Homework Equations A=1/2bh Height=Base The Attempt at a Solution A=1/2B^2 V=1/2B^2 from 0 to 3 V=1/2 B^3/3 from 0 to 3 V=B^3/6 from 0 to 3 V=27/6 please...

Homework Statement The area bounded by y=√x, the x-axis and the line x=9 and is perpendicular to the x axis. find the volume of the cross section using rectangle with the h=1/2b Homework Equations The Attempt at a Solution I just want to know if I'm correct or on the right track...

Homework Statement The only given data is that the cross section is 1m^2, the shape is circular (like a cut wire/rod) and i have to find the volume. Homework Equations from what I've searched, i found the equation: but i have no idea what to do with it, i still haven't learned it at...

Why is dot product given by a*b cosθ whereas cross product ab sinθ.

Homework Statement Cross sections are perpendicular to the x-axis and rectangle has the h=1/2b. The region is bounded by the area y=x^2, x-axis and the line x=3 Homework Equations The Attempt at a Solution A=BH A=B(1/2B) A=3/2B V=3/2(x^2-3) just wondering if this is correct...

Homework Statement What is the volume if the area bounded by y=x^2 and y=9 and the cross sections are perpendicular to the y axis Homework Equations The Attempt at a Solution I have no idea

There is a theorem stating the following: Let f be defined in a neighborhood of (x0, y0) in R^2. Suppose f has partial derivatives f_1, f_2, f_12, and f_21 in this neighborhood and that the cross partials f_12 and f_21 are continuous at (x0, y0). Then the cross partials f_12 and f_21 are...

I'm just wondering what the difference is between a cross section and a scattering cross section? Or is there any? I can't seem to find anywhere that clears it up, in fact there's a whole section on scattering cross sections in Kibble and Berkshire but they don't define it once :P

I am reading chapter three of Huang's Statistical Mechanics and I have a problem with equation (3.22). Having discussed the derivation of the classical cross section for a scattering process, Huang moves on to the quantum version of it. He states that in quantum mechanics the fundamental...

Homework Statement Suppose v is a vector satisfying: \alpha v + ( a \times v ) = b For \alpha a scalar and a, b fixed vectors. Use dot and cross product operations to solve the above for v. Homework Equations The unique solutions should be: v=\frac{\alpha^{2}b- \alpha (b \times a) + (b...

Homework Statement So I need to know how to attack a problem for a solid metal plate. The plate is used as a manhole cover, so it needs to withstand a certain load. The load is calculated by placing a large weight at the centre of area 25x25. I can't for the life of me figure out how to do...

The question is "Make a simple estimate of the order of magnitude of the ratio of the cross sections (electron,positron->2photons) and (electron,positron->3photons)" Now I know that cross section is proportional to (1/q^4)*(Phase space factor)*(Coupling constant) where q^2 = E^2 - p^2. We are...

Background: we're trying to show that the rate of change of angular momentum of an object about its center of mass (position given by R) is equal to the total torque about R. Why are the terms in red equal to 0? If anything, shouldn't the terms circled in in blue be equal to zero since the...

what is the cross section area of the water?? Homework Statement Determine an expression for the cross sectional area A of the fluid in the tank as a function of D and H. Homework Equations A=pi*r2 The Attempt at a Solution i try to let the radius equal to the height but then the...

Please Help. Trying my best Homework Statement Locate the Shear Center of the Cross Sections Below: 1. http://tinypic.com/r/98xfd3/5 2. http://tinypic.com/r/15s4hfk/5 Homework Equations τ=VQ/IT The Attempt at a Solution 1. Moment = O Solve for Ve τ=VQ/IT...

Yo does anyone have a table from like Brookhaven or somewhere of absorption cross sections for just about anything in the 1/v region? And have the precision included in the data. I'm doing a pretty quick statistics assignment.

Hello! I'm want to prove a vector identity for (\nabla \times \vec{A}) \times \vec A using the familiar method of levi-civita symbols and the identity \epsilon_{kij}\epsilon{kmn} = \delta_{im}\delta_{jn} - \delta_{in}\delta{jm}, but I don't seem to come up with any usefull answer. I...

I'm reading a book on microphones and came across the following: and then it goes off talking about something else... I feel stupid for asking this, but I don't get how the above equation works? For one, I thought cross products could only be be involving vectors? Aren't all the terms...

Hi all. This is my first time in the Physics Forums. I would like to ask for guidance in a calculation of a cross section of a process. I know the Feynman graph but I'm completely lost on how to start the calculation.. For example.. p p -> Z -> μμ Many thanks in advance..

Homework Statement A stiff wire 42.0cm long is bent at a right angle in the middle. One section lies along the z axis and the other is along the line y=2x in the xy plane. A current of 15.0 A flows in the wire-down the z axis and out the line in the xy plane. The wire passes through a uniform...

hey, i've been trying to work out how to determine the sign of cross products of unit vectors, for example in cylindrical, r x z = - theta theta x z = r r x theta = z i can't figure out the sign, r x z = |r||z|sinβ theta where β is the angle between them, which is 90°...

Hello. While I am not heading off to graduate school for a little bit, I am interested in persuing a phd in pure mathematics (Geometry is a broad interest of mine). I would also be interested in taking one or two mathematically inclined graduate courses from the Physics department (String...

this is a general question - the thing I'm working on if what i am asking makes sense - i am currently only looking for a confirmation on what i think is right this is a vector product question: if i have: (A/c x cB) can i look at that as: (1/c*c)(A x B) which comes to A x B the...

Homework Statement Let A = (-5, -2, -5), B = (-7, -7, -6), C = (-3, -3, 0), and D = (-5, -8, -1). Find the area of the parallelogram determined by these four points. Homework Equations Area of Parallelogram = ||a x b|| The Attempt at a Solution I drew the parallelogram and decided to use CA...

I'm numerically evaluating the differential cross sections \frac{\operatorname{d}\sigma}{\operatorname{d} \Omega} for e^{-}e^{+}\rightarrow\mu^{-}\mu^{+} scattering by integrating over \operatorname{d}\Omega = \operatorname{d}(\cos{\vartheta})\operatorname{d} \phi. Assuming no transverse...

Homework Statement Show that there is no vector ⃗e that has the property of the number 1 for cross product, namely that ⃗e × ⃗x = ⃗x for all ⃗x. Homework Equations I'm sort of stuck on how to show this. The Attempt at a Solution I set e=(e1,e2,e3) and x=(x1,x2,x3) and used cross...

Homework Statement Given |\vec{a}| = 8, |\vec{b}| = 9 and the angle between vector \vec{a} and \vec{b} is 48° find the cross product, \vec{a} X \vec{b}. Homework Equations Let θ = angle between \vec{a} and \vec{b}. \vec{a} . \vec{b} = ( \vec{x}1 * \vec{x}2 ) + ( \vec{y}1 * \vec{y}2 ) + (...

You have a fine wire with a cross sectional area of 9.4×10−10 m2 and a length of 1.1 m. You wish to determine what it is made out of, so you connect it to a standard AA battery (1.5 V) and measure a current of 0.048 A. What material is the wire most likely made out of? The options for the...

Calculating magnitude and direction of an magnetic force on an electron Homework Statement Okay so the question says that the magnetic force (Vector)FM on a particle which is in a magnetic field is found by (Vector)FM = Vector I x Vector B. Vector I = charge multiplied by the velocity of...

I recently saw the Evaluated Nuclear Data File provided by Brookhaven national lab., where in i saw the plot of "Neutron Energy Vs cross section (total)" for different elements. http://www.nndc.bnl.gov/sigma/index.jsp?as=1&lib=endfb7.0&nsub=10 Now what i am interested in is, can we derive or...