Cross Definition and 1000 Threads

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?

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...

I am looking for notes or a book that covers nicely the calculations for relativistic scatterings (Bhabba, Compton, pair annihilation, Moller, etc. ) Most QFT books, after explaining Feynman diagrams do not give too much details when it comes to cross section and decay rates. Often they put...

hello , can anyone give the formula of the differential cross section and the macro cross section because in each web i see a different notation thank you

Homework Statement #1 Given that the angle between the vectors a and b is 2Pi/3 and |a|=3 and |b|=4 calculate: (axb)^2 [(2a+b)x(a+2b)]^2 #2 Given three unit vectors, a, b, c such that a+b+c=0 find (a dot b) + (b dot c) + (c dot a) #3 Given AB=a+2b BC=-4a-b CD= -5a-3b...

Because it wanted to get away from the new PF member who called it his favorite fish! https://www.youtube.com/watch?v=2fr9bY0_JB8

Homework Statement 1. A vector u is given by u = λa + μb, where λ, μ are elements of ℝ. Calculate axu and bxu and show that: [(b χ u).n]/[(b χ a).n] = λ and [(a χ u).n]/[(a χ b).n] = μ (In any circumstance when I have omitted the underlining it is for convenience purposes, a, b...

Consider the cross section of two beams of same material as shown in the file attached. The area moment of inertia I about the central axis is equal for both the c/s. I have calculated it. Can somebody explain why the second c/s (2 in the figure ) is preferred for the design?

Homework Statement "Consider a wave plate with a retardation τ=(η_0-n_e)*w*L/c. Show that when it is placed between crossed polarizers with its optical axis at an angle of θ with respect to the polarizer axis, the transmitted intensity is given by: I_out/I_in= (sin^2(2θ)(sin^2(τ/2)) In...

Homework Statement consider the position vector expressed in terms of its cartesian components, r=xiei. Let w=wjej be a fixed vector whose components wj are constants that do not depend on the xi, so that δwj/δxi = 0 Homework Equations I am trying to evaluate ∇((wXr)^2) The...

I'm just learning this Latex(sic) formatting, so it's not ideal. I was trying to explore the geometrical significance of the cross product when I happened upon an interesting observation. I've seen things like this before, but never had time to really examine them. I define two vectors...

Homework Statement Find σ , the differential cross section, starting from the expression below and integrating over solid angle Ω Homework Equations dσ/dΩ = r2sin2θ The Attempt at a Solution dσ = r2sin2θ dΩ I remember that dΩ = sinθ dθ dμ and doing the μ integral from 0...

Hi, I was studying Maths the subject of Vector and found two important rule which are "dot" and "cross" product. I proved the first by myself with the (c^{2}= a^{2}+b^{2}-2.\|a\|.\|b\|.cosθ) However, the I couldn't make out how to prove the other one. I've been so thoughtful about it and need...

Another vector identity I have been trying to prove. My textbook lists this identity in "properties of cross products" without proving it. I have been trying to prove it, withou much luck, so some insight is appreciated. u \times (v \times w) = (u \cdot w)v - (u \cdot v)w Thanks! BiP

Anyone know how would I simplify a cross product where the two vectors have coefficients? For example (x/(y^3))\bar{r} X (x/(y))\bar{L} Thanks!

I wish to verify a couple of assertions. From the NNDC and other references, it appears that the neutron capture cross section of 3H (Tritium) is zero to a first approximation. This holds true for all neutron energies, including cold neutrons. These statements are equivalent to asserting that 4H...

the calculation of many quantities involve cross and dot products in their formulae. For cross products, i only know of three: lorentz force, angular momenta and torque. For dot products, i only know of one: work done im hoping to add more to my list. Can you guys help me include other...

Hello, How can I convert the number of events + the luminosity in a cross section? I think this must be trivial... thanks..

Homework Statement Calculate the cross product assuming that u X w = <-7,1,8> Find (-3u + 4w) X w = ? Homework Equations I'm not sure. I know you have to relate the cross product to something inorder to find what u and w are, but don't know what equations to use. The Attempt at a...

I understand how to calculate a vector cross product. I also understand that in order to calculate a vector cross product we are calculating the determinant of a 3 x 3 matrix. I guess I have a few questions. 1)How did mathematicians or physicists discover how to calculate the determinant...

Examine T= r x F (cross product), where |T|=|r||F| sin t, where t is the angle between r and F The intuitive idea of torque (let's only consider torque about the pivot for now) is that the stronger the force or the further away you are from the pivot point, the more the object will TEND to...

1. See attached image please! 2. For part (a), I applied the cross product and got (-6i - 2k) for (\vec{A}x\vec{B}. I got (6i + 2k) for (\vec{B} x \vec{A}). For part (b), \vec{C} was simply (-6i - 2k) - (6i + 2k) = (-12i -4k). For part (c), the magnitude of \vec{C} was simply 12.65 and for the...

Homework Statement 1. Suppose that u + v + w = 0. Show that u x v = v x w = w x u. What is the geometric interpretation of this result? (Note: The interpretation should explain both the length and the direction). 2. Let v1, v2, and v be three mutually orthogonal vectors in space. Use the...