What is Cross: Definition and 1000 Discussions

A cross is a geometrical figure consisting of two intersecting lines or bars, usually perpendicular to each other. The lines usually run vertically and horizontally.
A cross of oblique lines, in the shape of the Latin letter X, is also termed a saltire in heraldic terminology.
Throughout centuries the cross in its various shapes and forms was a symbol of various beliefs. In pre-Christian times it was a pagan religious symbol throughout Europe and western Asia. In ancient times, the effigy of a man hanging on a cross was set up in the fields to protect the crops. The cross was even considered a male symbol of the phallic Tree of Life; thus it often appeared in conjunction with the female-genital circle or oval, to signify the sacred marriage, as in Egyptian amulet Nefer with male cross and female orb, considered as an amulet of blessedness, a charm of sexual harmony.

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  1. M

    Vectors, angles, cross product

    Homework Statement Two vectors A and B have magnitude A = 2.99 and B = 3.10. Their vector product is A X B = -4.98 k + 2.08 i . What is the angle between A and B? Homework Equations C= ABsinθ C=A X B The Attempt at a Solution θ= arcsin C/(⎮A⎮⎮B⎮) so i found the magnitude...
  2. L

    Where does a radially falling test particle cross the inner horizon of RN BH?

    Hi, If a particle falls radially into a Reissner-Nordstrom BH with Q<M (i.e the case where you have an inner and and out horizon), then where in the conformal diagram does the test particle cross the inner horizon r_{-}? See for example the righthand Penrose diagram of...
  3. Kawakaze

    Solving Vectors: Find Dot & Cross Prods of OX,YX & OY,YX

    Homework Statement I already made a start to this question, the position vectors below are worked out in the first part of it, I am 99% sure they are correct so, on to the bit I am stuck on. :) A player stands with his feet at the point O and serves the ball from a point Y at a height of...
  4. P

    Is the Curl of a Cross Product Affected by Directional Nabla?

    I have a number of books which give a vector identity equation for the curl of a cross product thus: \nabla \times \left(a \times b \right) = a \left( \nabla \cdot b \right) + \left( b \cdot \nabla \right) a - b \left( \nabla \cdot a \right) - \left( a \cdot \nabla \right) b But doesn't b...
  5. E

    Mean free path and collision cross section

    Homework Statement I do need to calculate the mean free path for an ion with a radius of 9 x 10‐8 cm in pressures of 10‐8 Torr, 10‐6 Torr, 10‐4 Torr and 10‐2 Torr Homework Equations There are different equations I found but the most one is λ= 1/Nσ N gas number density which I do not...
  6. O

    Multidimensional cross product vector

    Does anyone knows how to compute cross product vector of more than 3 dimensions? It seems all the linear algebra textbooks only discuss 3D cross product vector. What are the formulas?
  7. A

    Differential cross section with invariant matrix element

    Homework Statement Calculate the differential cross section for A+B---> C+D with an invariant matrix element Homework Equations See attachment The Attempt at a Solution I have no idea how to even begin this problem. The course I am taking is an undergraduate course in intermediate modern...
  8. S

    Cross Product Identity: Solving for (A X B)^2

    I've been trying to find what the square of two cross products is and can't find it. Can anyone tell me the identity for (A X B)^2 ?
  9. M

    Solving Del Cross Question: Why is del x dB/dt = mu dJ/dt?

    Homework Statement I have to do an E&M problem, I think I got it, but I made a few steps that I don't really understand. The first one is: If delxB= muJ Does del x dB/dt = mu dJ/dt ?? If so, why ? I tried using latex, but it didn't work...sorry :( Homework Equations...
  10. L

    Find the volume of a solid using known cross sections?

    Homework Statement The base of a solid is the region between the parabolas x = y2 and x = 3 - 2y2. Find the volume of the solid given that the cross sections perpendicular to the x-axis are: a) rectangles of height h b) equilateral triangles c) isosceles right triangles, hypotenuse on the...
  11. R

    Calculating size of rectangle cross section

    Homework Statement A cmedium carbon steel rod has a rectangular cross section and must cope with a tension of 29 430 Newtons . The thickness of the rod is 15 mm calculate the siz of the cross section? Homework Equations A=P/Ok [b]3. The Attempt at a Solution [/b O = UTS = 750...
  12. J

    How to generalize determinant and cross product

    Assume that X^1,X^2,\ldots, X^k are vectors in \mathbb{R}^n, and 1\leq k\leq n. Is there a simple formula for the k-dimensional measure of the generalised "quadrangle" spanned by these vectors? If k=n, then the solution is |\textrm{det}(X)| with X_{ij}=(X^{j})_i. If k=2 and n=3, then the...
  13. L

    Cross product question find the magnitude of the force

    cross product question.. "find the magnitude of the force" Homework Statement A wrench 0.9 meters long lies along the positive y-axis, and grips a bolt at the origin. A force is applied in the direction of <0, 3, -2> at the end of the wrench. Find the magnitude of the force in Newtons...
  14. L

    Find theta from the cross product and dot product of two vectors

    Homework Statement If the cross product of vector v cross vector w = 3i + j + 4k, and the dot product of vector v dot vector w = 4, and theta is the angle between vector v and vector w, find tan(theta) and theta. Homework Equations vector c = |v||w| sin(theta) where vector c is the...
  15. A

    Perpendicular vector using dot not cross product.

    Homework Statement I have 2 (3d)vectors A and B and I want to find a vector C perpendicular to both of them. A = 3i-2j+4k B = -2i+5j-2k C = Cx+Cy+Cz Homework Equations So we know A dot C = 3Cx-2Cy+4Cz and B dot C = -2Cx+5Cy-2Cz The Attempt at a Solution
  16. S

    Cross Product and Normal Vector Related Question

    Homework Statement Find the distance from the point (2, 4, 4) to the line x = 0, y = 4 + 3t, z = 4 + 2t. Homework Equations The cross product and the dot product and d = |n * b|/|n| The Attempt at a Solution So the distance from the point to the line is the line directly...
  17. Q

    Dot product between cross products

    Homework Statement show (axb) . (cxd) = |a.c b.c| |a.d b.d| The Attempt at a Solution i have no idea. i don't know if the lines at the side are modulus lines or matrix brackets but it seems that it has something to do with distribution law. but i can't start proving if i...
  18. R

    Cross sectional area - Young Modulus

    out of interest does cross sectional area change when a force is applied (lets say I had a wire and I applied a force to it, the wire would stretch ) does its cross sectional area change
  19. T

    Finite and infinite cross sections

    The cross section for scattering by a Coulomb potential 1/r is the same for both classical and quantum mechanics, and the total cross section is infinite. I understand this classically as saying that no matter how large an impact parameter an incoming particle has, it will still be deflected at...
  20. quasar987

    Homology cross product and orientation

    An orientation of a real n dimensional vector space V is an equivalence class of an ordered basis. Equivalently, this corresponds to a choice of a generator of H_n(V,V-0)=Z. The correspondence between the two is this: given an ordered basis (v_1,...,v_n) of V, the convex hull of...
  21. E

    Cross Product of Curl Identity

    Hi, I've been trying to derive the electromagnetic stress tensor on my own, and I've run into a bit of a problem. I have a cross product of a curl (\vec{E}\times(\nabla\times\vec{E})) that I need to expand, and the typical...
  22. C

    Vector Cross and Dot Products: Understanding and Solving Problems

    Hey guys, I'm a kinda noobie to this site so I have not much experience with the formatting and stuff here, but anyway was doing some physics and came stuck =P Would really appreciate any help Homework Statement Vectors A and B are drawn from a common point, with the angle in between them...
  23. L

    Question about cross and dot product

    Homework Statement There are two points p1 pointing up p2 pointing rightHomework Equations The Attempt at a Solution I need to find \stackrel{\rightarrow}{p1} * r^ \stackrel{\rightarrow}{p2} X p1^ \stackrel{\rightarrow}{p2}* r^ they got \stackrel{->}{p1} * r^ =0 why is that? i know...
  24. L

    Understanding Torque and Cross Product Calculations for Dipoles

    Homework Statement This is a physics problem. need to find torque on dipoles the the 2 dipoles are on the same plane with distance r p1 is pointing up while p2 is pointing right Homework Equations N=PxE The Attempt at a Solution I know how to do a cross product, you make the...
  25. N

    What is the relationship between the torque and position vectors?

    A 5.0 kg object at r= i^+2j^+3k^ meters has an acceleration a=5i^+6j^-7k^ m/s^2 a)what is the objects torque around the origin of the cordinate system b)prove that the torque is perpendicular to the position vector r a) t^=rXma=-10<16,-11,2> t=-10(381)^1/2 b) <1,2,3>*<16,-11,2>=0
  26. J

    Cross product order of operations

    Could someone please clarify a simple order of operations related to cross product? A x (B x C) = ? I am not sure between the these two options: = (A X B) x (A X C) or = do stuff in parenthesis first then cross with A
  27. N

    Dot product, cross product, Newton's laws.

    My final for Physics is coming up and I really, really ****ed up in this class. I don't even know how to do dot products, cross products, or let alone Newton's laws. We applied Newton's laws to some pulley problems I think. I've been going to all the lectures but it just doesn't stick -- nothing...
  28. V

    Expressing a variable from cross product

    Can I use cyclic rotation in \vec{a} = \vec{b} x \vec{c} and say: \vec{c} = \vec{a} x \vec{b} \vec{b} = \vec{c} x \vec{a} for any vectors \vec{a}, \vec{b} and \vec{c} or only if they are perpendicular to each other? If it's only a special case: is there a way to express \vec{b} and...
  29. H

    Can I Calculate Traces and Cross Sections in QED Using Gamma Matrices?

    hi how to calculate the traces of product of Dirac matrices in QED. i want caculate crossection of process scattering in QED. a program to calculate it
  30. R

    SolidWorks FEA (Varying Cross Section)

    Does anyone know how SolidWorks calculates the stresses for this simulation. Can anyone give me an idea, is it second moment of area? y/r = m/i? Thanks Richard.
  31. T

    Show this equality of limits - cross products

    Homework Statement Show that \displaystyle\lim_{\underline{h}\to 0} \frac{\underline{c} \times \underline{h}}{\|\underline{h}\|} =0 where c and h are vectors and x denotes cross product. Homework Equations The Attempt at a Solution No idea how to do this?
  32. D

    Cross Product of i x -i: Answer?

    Homework Statement cross product of i x -i Homework Equations i x i =0, i x j = k, etc. The Attempt at a Solution I'm guessing it would be zero, just making sure because I keep getting the question I'm working on wrong.
  33. C

    The difference between microscopic and macroscopic cross sections.

    Hello there folks. So I'm doing some homework, and one of the questions asks for a comparison of the microscopic absorption cross sections of B, Cd, Gd, and Hf with the fission cross section of U-235. I've found the fission cross section in my trusty 17th edition of Nuclides and Isotopes, but...
  34. T

    What Determines the Cross Sectional Flow Area in Air Ducts?

    I was ask to find the Cross Sectional Flow Area of a air duct given this question : The air duct is a vertically mounted duct of 65mm by 150mm cross-section and approx. 1.2m long. My working is like this: 65 x 150 = 9750mm2 I just wanted to clarify if my working is right. Another...
  35. U

    How to solve cross products in physics problems?

    Homework Statement I'm solving a physics problem using cross products and I think I might be doing the cross products wrong Homework Equations I'm using the formula: a cross b = (a2b3- a3b2)x + (a3b1- a1b3)y + (a1b2- a2b1)z where a1 = ax, a2 = ay, a3 = az, etc. I don't know if this...
  36. D

    Photon interaction cross section? What?

    Photon interaction cross section? What?!? Hey guys-- I'm practicing for the GRE, and I came across a question that has stuff that's not even in my textbook! I haven't found much from googling either. Here is the question: My instinct was to guess (C) because graphs I had seen of the...
  37. N

    Intersection of planes using cross product

    Hello! I have a quick question regarding the intersection of three planes if the determinant is 0. If there are solutions, there will be an infinite number of solutions. One of the equations for the plane can be ignored as it is a linear combination of the other two, and can be ignored for...
  38. F

    Florentz Force = Fmag + Felectric: Cross Product Sum

    If Fmag = q(v x B) and Felectric = qE, Florentz = q [E + (v x B)] can I say that Florentz = Fmag + Felectric?
  39. Ivan Seeking

    Stargazing Aug 21st, 2017, a total solar eclipse will cross the US

    And goes directly through Oregon. Woohoo! http://eclipse.gsfc.nasa.gov/SEgoogle/SEgoogle2001/SE2017Aug21Tgoogle.html
  40. MathematicalPhysicist

    Cross fertilization between string and non string approaches.

    Do you know people who work in both string and non string QGs, or who changed from string to non string or vice versa?
  41. M

    How to calculate torque with cross product?

    Homework Statement A rod has one end at the origin and one end at the point P whose coordinates are (1m, 2m, 2m). A force F = (3i+2j-1k) N acts on the rod at the point P. What is the torque about the origin due to F? Homework Equations torque = F x r The Attempt at a Solution I'm...
  42. N

    Cross product associative triples

    cross product "associative triples" Homework Statement We know that the cross product is not associative, i.e., the identity (1) (\vec{a}\times\vec{b})\times\vec{c} = \vec{a}\times(\vec{b}\times\vec{c}) is not true in general. However, certain special triples \vec{a};\vec{b};\vec{c} of...
  43. M

    Cross product ,why doesnt this work

    Homework Statement A= ci-2j+k B=i+2j-k Find c that makes the vector(A-B) perpendicular to the vector B Homework Equations AXB = (AxBy-AyBx)k+(AzBx-AxBz)j+(AyBz-AzBy)i The Attempt at a Solution A-B=(c-1)i-4j+2k I said that since (A-B) is perpendicular to B then |A-B| * |B| =...
  44. H

    What do dot and cross product mean in electromagnetics?

    Hello. I am taking a fundamentals of electromagnetics. There are couple of formulas I have been using without understanding the concepts. \nabla \cdot B = 0 \nabla X E = 0 (curl free) In those cases, what do dot and cross product mean? Thanks.
  45. M

    Vectors dot product and cross product help

    Homework Statement Vectors A and B (both with the lines over it) lie in an xy plane. Vector A has magnitude 8 and angle 130 degrees, Vector B has components Bx=-7.72 and By=-9.2. a)What is 5(vector A) dot vector B? b)What is 4(Vector A) cross 3(vector B) in unit vector notation and magnitude...
  46. B

    How Is Differential Cross Section Defined in Physics Experiments?

    Homework Statement a) Define the differential cross section \frac{d\sigma}{d\Omega} in “experimental” terms, i.e., in terms of the number of scattered and incident particle. b) Show that for a situation in which there is a scattered wave f^+\left(\theta\right)\frac{e^{ikr}}{r} asymptotically...
  47. R

    Finding the Cross Product in R2: How is it Different from R3?

    How do you find the cross product when you are given two vectors in R2? i know how to do it for R3
  48. M

    Finding cross product of two vectors a,b

    Homework Statement A vector of magnitude 17 units and another vector of magnitude 7.4 units differ in directions by 27°. Find (a) the scalar product of the two vectors and (b) the magnitude of the vector product ×. Homework Equations Right-hand rule, a*b=abcos(theta), A x B=...
  49. G

    Design a tension member w/ cross section

    design a tension member w/ cross section... Homework Statement You are to design a tension member (square rod) with a cross section to carry a mass of 575 000 kg with a safety factor of 2 against yield and a safety factor of 3 against static fracture (overload). a) What is the design...
  50. B

    Properties of cross and dot products

    Homework Statement let u be a nonzero vector in space and let v and w be any two vectors in space. if u.v = u.w and u x v = u x w, can you conclude that v=w? give reason for your answer. Homework Equations The Attempt at a Solution v is not necessary equal to w since u is nonzero...
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