Cross Definition and 1000 Threads

Homework Statement find B from F=q(v X B), where F is magnetic force, q = charge, v = velocity, B = magnetic field. Carrying out 3 experiments, we find that if v_1 = i, (F/q)_1 = 2k - 4j v_2 = j, (F/q)_2 = 4i - k v_3 = k, (F/q)_3 = j - 2i where i,j,k are the unit cartesian vectors This...

I'm calculating an ionization cross section in partially ionized plasma, with taking into account of correlation effects. I'm trying to do it with help of variation phase method. Please, help me to find some link to useful articles.

Suppose that a particle's position is given by the expression in the attachment Explain: 1. When does the particle first cross the negative x axis? 2. Find the particle's velocity as a function of time. Express your answer using unit vectors.(e.g., A i_unit+ B j_unit, where A and B...

Homework Statement Given that A = 2i + 4j, evaluate each of the following. (Hint: This question can be answered without computation.) (a) What is AxB when B = 8i + 16j? (b) What is AxB when B = -8i - 16j? Homework Equations AxB=(Axi + Ayj) x (Bxi +Byj) =(AxBx)(i x i)...

I'm having trouble relating the cross product form |a||b|sin(theta) to its component form (a1b2 - a2b1) ... and so on... I know how to do this mathematically so please don't just suggest some proof that I can find in every textbook... The component form involves the solutions to equations...

1. How do you find the current if it tells you how many electrons pass through cross section of a conductor each second 2. ... 3. ...I don't know the first thing to do about this. Just the number of electrons make me think of the equation Q = Ne ..but charge doesn't have to do with...

Homework Statement A signal x(t) is transmitted and received back as y(t) and sampled in the receiver, so we get a DT signal y[n] = ax[n-D] + w[n], where w[n] is noise baiscally i need to explain how we can measure the time delay by computing crosscorrelation Ryx(l). My undestanding is...

Homework Statement Show that AXB is not equal to BXA No variables given..just this equation Homework Equations The Attempt at a Solution I don´t know how to start...the only thing I know so far is that AXB is equal to -BXA

Homework Statement I hope I am not posting this question at the wrong place, but can someone explain to me the vector product rule, or cross product rule. I don't seem to get the hang of it. Why I am asking this is because I want to know how force on a moving charge due to an applied...

I was wondering whether there's any interactions or productions that has cross section that doesn't only increase monotonously with energy, but has a drop somewhere at certain energy scales ?

Homework Statement In Calculus on Manifold pp.83-84, Spivak writes that "if v_1,...,v_{n-1} are vectors in R^n and f:R^n-->R is defined by f(w)=det(v_1,...,v_{n-1},w), then f is an alternating 1-tensor on R^n; therefore there is a unique z in R^n such that <w,z>=f(w) (and this z is denoted v_1...

Homework Statement Given the two vectors written in component-unit vector form below: D = 3\hat{i} - \hat{j} E = 2\hat{i} + 4\hat{j} a.) Find the unit vector in the same direction as D b.) Find the cross product of D x E c.) Write the vector D in magnitude direction form Homework...

After I graduate from college I planned to drive across the United States on my little chevy and tour all the US landmarks and experience the taste of the regional food while on the way to graduate school. My only primary worry is how expensive it will be to travel across the country if from...

This is probably a very dumb question, but I'm stuck with it. The cross sections one finds on http://www.nndc.bnl.gov/sigma/ as a function of incident energy, is that energy given in the lab frame or in the cog frame ? For heavy a nuclide, this doesn't matter, but for hydrogen for instance ...

Hi all, I have a qustion. dB/ds= -TN, dU/ds= KN (1) N= U x B (2) dN/ds=TB-KU (3) How Eq.(3) can be obtained from Eq.(1),(2)? Have a nice day!

Homework Statement A centripetal-acceleration addict rides in uniform circular motion with period T = 3.22 s and radius r = 3.00 m. At one instant his acceleration is a = (7.00 m/s2) i + (-9.00 m/s2) j. At that instant, what are the following values? (b) r X a The Attempt at a...

Homework Statement I'm working on a problem that is asking me to find Young's Modulus. I have the right formula and everything that I need but I can't seem to figure out how to find the cross sectional area of a nylon rope. The rope is 21 m long and 1.4 cm in diameter. Homework...

Hello, I'm reading a classical mechanics book. In it, they show a derivation of the centrifugal force equation: \vec{ F_{\textrm{cf}}} = -m \vec{ \omega } \times \left( \vec{ \omega } \times \vec{ r } \right) I understood the derivation up to that point. However, they have a couple additional...

Hy guys, i don't know if this is the best place to post this... so this is my question: where i can found a good resource for cross sections and decay rate? i mean a book with many calculated cross sections or web sites. thank you.

Why is it possible to take the cross product in only 3 and 7 dimensions?

The Einstein cross (G2237+030) shows 4 reasonably symmetrically spaced images of the very distant quasar, indicating that our alignment with the galactic nucleus to quasar line is fairly good. How is that it does not show an Einstein ring instead of the cross?

Use two methods to determine a unit vector perpendicular to both (2,1,-3) and (-1, 7, 4) Using Cross Product: Let v be a perpendicular vector to the given vectors v = a*b = (2,1,-3)(-1,7,4) =((1)(4)-(7)(-3), (-3)(-1)-(4)(2), (2)(7)-(-1)(1)) =(4+21, 3-8, 14+1) =(25, -5, 15) = (5, -1...

I need to show: (\mathbf{\sigma} \cdot \mathbf{a})(\mathbf{\sigma} \cdot \mathbf{b})=\mathbf{a} \cdot \mathbf{b} I + i \mathbf{\sigma} \cdot (\mathbf{a} \times \mathbf{b}) where a and b are arbitrary vectors, sigma is the pauli spin operator. I was just wondering what the dot product...

2 questions i have; 1. proove that; p x ( q + r ) = p x q + p x r 2. and p x ( q x r ) = ( p x q ) x r where; p = p1i + p2j + p3k q = q1i + q2j + q3k r = r1i + r2j + r3k

How are the exterior products and the cross products related? Wikipedia says: "The cross product can be interpreted as the wedge product in three dimensions after using Hodge duality to identify 2-vectors with vectors."

A charged particle moves through a region of space containing both electric and magnetic fields. The velocity of the particle is v = (3.3 x 10^3 m/s) x + (2.7 x 10^3 m/s) y and the magnetic field is B = (0.81 T) z. Find the electric field vector E necessary to yield zero net force on the...

ok, i don't know what to do with something like this: (d^2R/dt^2 ) + (dR/dt) x B = 0 where the capitals are vectors (sorry i suck at latex). R is a position vector in x-y plane and B is in the z-direction. do i split this into equations for x and y directions separately and solve them...

Hi guyz, I have a small question, In spherical coordinates if we define 2 vectors such as magnetization of a shell M(r,phi,theta) and the magnetic field H(r,phi,theta) As we know the cross product between them is written in the determinant: (Capital means unit vectors) det[(R,r...

Homework Statement The total cross section of a S wave is given by the following equation Sigma=(pi/k)*(b^2)/((E-En)^2+(b/2)^2)) prove that b is the width of the resonance. Homework Equations Nothing that is the only thing The Attempt at a Solution I already solved the question...

hi all. my homework question is what is the derivative of: [(a + t * b) x (a + t * b + t^(2) * c)] a, b, and c are vectors, and t is a constant. * is multipy, ^(2) is squared, and x is cross product. i've been working on it for hours and i have no idea what to do. there's another similar...

While taking linear algebra I never really understood where the dot and cross product came from. It seemed that they were just randomly defined. I know that the dot product is an inner product but why is it defined as: \vec v \cdot \vec u = v_1 u_2 + v_2 u_2 ? why not \vec v \cdot \vec u =...

For my diploma thesis I must provide a calculation that reproduces the results given on page 46 of the paper hep-ph/0309342 . For those who do not want to look it up, I briefly explain what it is about: It concerns the two-body scattering processes (1) N + V => L + H, (2) N + L => V + H, (3) N...

I didn't use the template, because I am not having difficulties with a problem. I am just starting to study rotational motion and there it appears the cross-product. I don't like to memorize formulae that I don't understand it's meaning. Why is \vec a \times \vec b} defined mathematically...

[b]1. When the hot water in a certain upstairs bathroom is turned on, a series of 18 "ticks" is heard as the copper hot-water pipe slowly heats up and increases in length. The pipe runs vertically from the hot-water heater in the basement, through a hole in the floor 5 m above the water heater...

What vector space are cross products done in?

In a scattering experiment, an aluminium foil of thickness L = 10E-6 m is placed in a beam of intensity of 6E12 particles per second. The differential scattering crosss section is known to be of the form. \frac{d\sigma}{d\Omega} = A + Bcos^2 (\theta) where \theta is the...

A particle position is described by position vector r = 3i + 2j and the force vector i - 2j acts on the object. 1) Find the torque about an axis through the origin and perpendicular to the xy plane. Draw the two vectors to check your torque direction. I used the right hand rule and found...

Ok, this one has really got me... Suppose that u \centerdot (vXw) = 2. Find (a) (uXv) \centerdot w (b) u\centerdot(wXv) (c) v\centerdot(uXw) (d) (uXv)\centerdotv Once I understand the what to do with the information given, I am sure the rest of the problems will fall into place...

In R^3 it is easy to compute the cross product, and i know how to compute it in higher dimensions using wedge product and the hodge star, which shows that it only exists in 3n dimensions. My question is given two vectors in C^3 (complex), is there a neat way to find one perperdicular to...

My book says self pollination maintains the parental characters or purity of the race indefinitely and is used to maintain pure lines for hybridization experiments. How can that be true. Coz, meiosis takes place in micro & mega spore mother cells. So there is crossing over which will lead to...

I am supposed to solve this explicitly for x: x=(x x A)+B where all variables represent vectors. I moved the B vector to the other side and I was thinking i can take a cross product of something with each side to isolate x but do not know what works here, i tried crossing both sides with...

If I show something that a cross section is proportional to: 1 / (16p^2 sin^4( x) + 8mpsin^2 (x) + m^2) does it imply that the cross section is proportional to 1 / sin^4 (x) as well?

Hey guys, I will admit that I am having extra troubles on this chapter and I don't understand most of it so be gentle :\. Anyways I realize these problems are porbably easy but here they are: 1) A Load of 140,000 N (31,500lbf) is applied to a cylindrical specimen of a steel alloy that has a...

Is the fact that \vec{a}\times\vec{b} = \det \begin{bmatrix}\hat{e}_1& \hat{e}_2 & \hat{e}_3 \\ a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \end{bmatrix} just a coincedence (ie. a mneminic device) or does it have some deep mathematical significance? edit: Also, is the cross product, like the dot...

Hello, my problem is as follows: Given that A and B are known vectors, and A \cdot C=u is a known quantity, and A \times C=B Express C in terms of A,B, u, and the magnitude of A So far what i have done was use the definition of the dot product as AC cos \theta=u, and cross product as AC...

This is the question: Two vectors A and B have magnitude A = 3 and B = 3. Their vector product is A X B = -5k+2i. What is the angle Between A and B. OK so I'll start with what I do know. I do know that the cross product is the magnitude of A times magnitude of B times sin theta of B. I end...

Sometimes we need to know the ratio of the capture section and recocmbination cross section of the electron or hole. for example, to identify the mechanism of phosphors, it's very important to know the ratio to analyze the process of luminescence. The question is how we identify the ratio, from...

When you swim across a river does the time to reach the opposite shore depend on the rate of flow of the water? Defend your answer

I have my thesis defence tonight at 17h CET. :biggrin: If you like, I've put the presentation online http://www.geocities.com/dimitri_terryn/Presentatie_thesis.ppt It's in Dutch, but I will translate it when I have the time (i.e. after graduation).

Can some one help me out here, I'm stuck on the following problem: show that four distinct points z_i , i=1,\ldots,4 in \hat{\mathbb C} lie on a circle in \hat{\mathbb C} if and only if the cross-ratio \left[ z_1,z_2,z_3,z_4 \right] is real. So, I know we can write the...