Cross Definition and 1000 Threads

Homework Statement i) Find all vectors v such that <1,2,1> X v = <3,1,-5> ii) Explain why there is no vector v such that <1,2,1> X v = <3,1,5> Homework Equations a X b = <a_{2}b_{3} - a_{3}b_{2}, a_{3}b_{1} - a_{1}b_{3}, a_{1}b_{2} - a_{2}b_{1}) The Attempt at a Solution i) <1,2,1> X v =...

Homework Statement Find a plane perpendicular to the two planes, X+Y=3 and X+2y-z=4 I know i take the cross product of both so i get <1,1,0> and <1,2,-1> But when i do the cross product i get x-y+z book tells me x-y-z what am i doing wrong? Not sure why the z is negative. The...

Homework Statement Not really a homework problem, just a general question. Homework Equations Sorry, I don't yet know how to create arrays/matrices in latex (this is a gif) The Attempt at a Solution In the above image, why is c_{1} positive, c_{2} negative, and c_{3} positive? Aside from...

Homework Statement Using conductivity constant (q=1.45*10^6mA) deduce the cross-Sectional area of the wire from the slope of the Data found in the graph. Voltage was kept constant 1.00 volts The wires are each 1m long After graphing the data the Current(mA) # of parralel lines 121.4...

Use cross product formula in R^4 to obtain a vector that is orthogonal to rows of A Please help with first part and check if i answered the questions correctly. The matrix A = 1 4 -1 2 0 1 0 -1 2 9 -2 2 1. Use cross product formula in R^4 to obtain a vector that is...

Homework Statement Leta theta be the angle between the vectors u=2i +3j -6k and v=2i + 3j+6k A) use the dot product to find cos theta b) use the cross product to find sin theta c) confirm that sin^2(theta) + cos^2(theta)=1The Attempt at a Solution I got a to be 117 degrees, but however b and c...

Homework Statement The base is the semicircle y = \sqrt{9-x2}(Square root of 9-x2.. i don't know why the formatting isn't showing up) where -3 <= x <= 3. The cross section perpendicular to the x-axis are squares. Homework Equations -3\int3 = A(y)dy A(y) = area of cross section...

Recently, I had lab. In the lab we took different objects and measured their strain. One object had a varying cross section. The data for strain was recorded. Right now, I'm trying to make a stress strain graph, but the problem is my equation for stress. I don't know how i can take my moment of...

Homework Statement Given a = <1,2,3> and b = <1,-1,-1>, sketch the collection of all position vectors c satisfying a x b = a x c Homework Equations The Attempt at a Solution I've calculated a x b = <1,4,-3> and Defining c = <x,y,z> I found a x c = <2z-3y, z-3x, y-2x>. I want to...

[b]1. For two differentiable vector functions E and H, prove that (Delta (dot) (e X h) = H (dot) (delta X e) - e (dot) (Delta X h) [b]2. Cross product and dot product. The Attempt at a Solution First I took did the left side of the equation, I took the cross product of vectors e and...

I would like to check my answers... Homework Statement Given nonzero vectors u, v, and w, use dot product and cross product notation to describe the following. A vector orthogonal to u X v and u X w A vector orthogonal to u + v and u - v A vector of length |u| in the direction of v...

from what I know: cross section in particles physics can be seen as throwing random darts on ballons on a wall, ie the wall is stationary. but if I want to work out the cross section of two laser beams at certain angles, the analogy above wouldn't hold would it? Since photons can never to...

Homework Statement Describe all unit vectors orthogonal to both of the given vectors: \vec{a} = 2\vec{i} - 4\vec{j} + 3\vec{k} \vec{b} = -4\vec{i} + 8\vec{j} - 6\vec{k}Homework Equations The cross product of two vectors using the determinant, then dividing by the magnitude of the vector...

Homework Statement show that: ( a - b ) x (a + b ) = 2a x b and wat is its geometric interpretation ?? I'm not sure what's wrong, but i somehow got the value as 2a and not wat was required... PLease help. Homework Equations Since this is a proof, the answer I've arrived at is...

i know that del.v=divergence of vector v and del x v=curl of vector v can anyone justify for the same? how dot product is physically connected to divergence property?

In particle physics, what is a differential cross section? I think I understand what a cross section is, but I can't find any information on what a differential cross section is. I don't see how a cross section could be differentiated.

Homework Statement I eventually have to solve for maximum angular acceleration of the loop in a magnetic field, and I have gotten everything with the exception of the moment of inertia, so I won't include the emf and B known variables. Known: a copper wire with a density of \rho = 8960...

hi i am currently looking for a derivation of the differential cross section, that is not an abuse of mathematics, cause all derivation i found use differentials that are treated like fractions and so on? greetings Gavroy

Homework Statement A medium carbon annealed steel rod has a rectangular cross section and must cope with a tension of 3 tonnes. The thickness of the rod is 15mm. Calculate the size of the cross section. Homework Equations ? The only formula I know with CSA and force is: stress = Force...

I'm trying to do an integral, in which the integrand is composed of arbitrary functions and contains a derivative of the variable of integration. Further still, the integral is over a discontinuity. Because these are arbitrary functions I assume there is no exact solution, but I'm looking for...

he question asks to find the ratio between E0 and B0 and the ratio between w and k ? E and B are on the x-y plane they are given as verctors without any components dividing no x direction part,y direction part,z direction part so when when i use the maxwell equations \nabla\times...

Hi all. I'm working on a project at the moment, and I've run into some questions regarding the 4-d Levi Civita tensor contracted with the metric tensor. I'm working on finding the cross-section for neutrino-proton scattering. While ccontracting the hadronic and leptonic tensors, I end up...

I am inquiring as to what the theorem function is for the mean product of cross section and velocity for stellar fusion reactions? \langle \sigma v \rangle Mean product of nuclear fusion cross section and velocity. \langle \sigma v \rangle Maxwell–Boltzmann probability density function: f(v)...

Can someone please explain to me the motivation for these definitions of the cross product? Let A = (a1, a2, a3), B = (b1, b2, b3). Let A and B be the magnitudes of A and B, respectively, and let \theta be the angle between the vectors. A X B = AB sin(\theta) A X B = (a2b3 - a3b2, a3b1...

What is a cross over? It seems to be something like a "qualitative change" without a phase boundary, in the vicinity of the end of a phase boundary. But what is the proper definition? How is it different from other sorts of continuous changes? Is it something that an experimentalist can detect?

Homework Statement It's not a homework question but a doubt I have. Say I want to write \vec A \times \vec B in the basis of the cylindrical coordinates. I already know that the cross product is a determinant involving \hat i, \hat j and \hat k. And that it's worth in my case...

Hi. Can somebody recommend a good book (advanced level) dealing with applications of cross correlation functions? I mean what kind of conclusions can be drawn etc?

Homework Statement Find the angle between \begin{align*} \vec{A} = 10\hat{y} + 2\hat{z} \\ and \\ \vec{B} = -4\hat{y}+0.5\hat{z} \end{align*} using the cross product. The answer is given to be 161.5 degrees. Homework Equations \left| \vec{A} \times \vec{B} \right| = \left|...

Homework Statement Find a linear transofmration from X={x1,x2,x3} to U={u1,u2,u3} which will remove the cross product term in the quadratic form of equation 2X12+4X22+5X32-4X1X3 and thus write the resulting quadratic form in u1,u2,u3. Homework Equations The Attempt at a Solution No...

So I have been reading about the cross section of neutron capture and have been reading about how the cross section for neutrons in a given material depends on neutron energy, the most important factor obviously. But I have not seen as much information on how, for a neutron of a given thermal...

Homework Statement The Femur bone in the human leg has a minimum effective cross section of about 3.0 cm2 How much compressible force can it withstand before breaking Homework Equations Compressive Strength (bone)(N/m2) = 170 x 106 P = F/A The Attempt at a Solution Not sure what a...

Homework Statement base of a solid is bounded by y=\sqrt{x}, the x-axis, and x=9. each cross-section perpendicular to the x-axis is a semi-circle. find the volume of the solid Homework Equations The Attempt at a Solution I found the answer to be 81\pi/16 by the following steps...

Homework Statement Given A . B=0 and A x C=0...whats the angle b/w B and C? Homework Equations The Attempt at a Solution..

Does the absorption cross section to scattering cross section ratio of an isotope vary with neutron energy or stay constant? I have heard that cross sections in general are inversely proportional to velocity (eg the fission cross section of U235 is about 1000 times higher for thermal neutrons...

Ok, although I had hoped to avoid having to ask a stupid question, it seems as though I'm just too dense to figure this one out on my own. Generally I can, with the help of Google, and the combined wisdom of the internet, deduce an answer. But either Google, the internet, or my brain has failed...

Homework Statement \iint \mathbf{F} \cdot \mathbf{dS} = \iint \mathbf{F} \cdot |\mathbf{r_u} \times \mathbf{r_v} | \mathbf{dA} = \iint \mathbf{F} \cdot |\mathbf{r_u} \times \mathbf{r_v} | \mathbf{\hat{n}}dA = \iint \mathbf{F} \cdot |\mathbf{r_u} \times \mathbf{r_v} | \frac{\mathbf{r_u}...

Homework Statement In Problems 1-5, let R be the region bounded by y = x^2 + 3, y = 2x, x = 0, and x = 4. Each problem will describe the cross sections of a solid that are perpendicular to the x-axis. Write an integral expression that can be used to find the volume of the solid (do not...

Hi. I've been studying for a test and have been scouring my text for methods of proving points in 3-dimensional space are collinear. The best I can see is that the cross-product of the vectors must equal zero. Can someone explain how to do this a little more clearly?

Homework Statement Note: \nu is del could not find it... I need to prove the \nu*E=0 and \nu x E=-dB/dtHomework Equations E(s\phizt)=(Acos(Kz=wt)/s)s^ The Attempt at a Solution so for the first one \nu*E=0 I thought it would be d/ds(E) but what they did was 1/s d/ds(s E) no idea why they...

Homework Statement 2 projectiles, one at the origin the other at (0,100,0)m, have initial speeds of 35 m/s and 55 m/s respectively, and have direction cosine angles (45,60,60) and (60,135,60) respectively. Both are under the influence of gravity and experience a force of air resistance that...

Hey, I have a problem that can be written in the following form: u=v x w where u, v, w are 3by1 vectors and x is the cross product. now I want to write v in term of u and w, but I have no idea of how to get vector v out of the previous equation. Someone who can help me with this...

Tornados and storms have caused 200 fatalities during the last two days. Several towns in 5 states were hit. Tuscaloosa Mayor Walt Maddox stated that "hundreds of businesses and homes were destroyed." In April, more than 800 tornados have been recorded. Apparently this shatters the old...

hi guys, I was wondering what is the equation of cross section between fuselage and wing of the below airplanes:antonov 140 , B-707 , cessna-210 , cessna citation. Can anyone help?a book or a refrence or whatever you have

hi guys, I was wondering what is the equation of cross section between fuselage and wing of the below airplanes:antonov 140 , B-707 , cessna-210 , cessna citation. Can anyone help?a book or a refrence or whatever you have

Hi, This is my first post. Sorry for the mistakes it certainly contains. I have two questions. First, is there a tutorial for using embedded LaTex? I found some general tutorials on LaTex, but I couldn't get some of the commands listed in that tutorial to work in the embedded LaTex code...

Knowing: u * (v x w) = 5 where u, v and w are vectors. What is [Proj u (v x w)] * u Ive been staring at the dot and cross product properties in my book for a while and I don't see how to do it.

So, the other day, I was learning about Scalars and Vectors and about Dot product and Cross Product. Now, in Cross Product, I was just thinking, when my thought slipped on the following stone: What is the physical implication of => aXb(cos\vartheta) ? I mean, how would you represent it on a paper?

Hi everybody, I have a experimental question. In cross-section calculation of production of particles (say D), one counts the number of produced D. To selection the D one has to apply some kinematic cuts. If cuts are tight, number of D will be less and if cuts are loose, number of D will be...

Does anybody know of any good references that explain the concepts/mathematics behind cross sections particularly well? Websites, textbooks, whatever...

Homework Statement A thin (1mg/cm^2) target of 48-Ca is bombarded with a 10-nA bean of alpha particles. A detector, subtending a solid angle of 2E-3 steradians, records 15 protons per second. If the angular distribution is isotropic, determine the total cross section, in mb, for the reaction...