Cross Definition and 1000 Threads

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. W

    How Do You Calculate Genotype and Phenotype Ratios in a Trihybrid Cross?

    Homework Statement How would you figure out the genotypes and phneotypes if you Cross TTBbRr with TtbbRr? Trihybrid cross Homework Equations Cross TTBbRr with TtbbRr The Attempt at a Solution I did the crossing, but i don't know how to do the genotypes nor the...
  2. Ƒ

    Understanding Dot and Cross Products: Key Concepts Explained

    Not so much an actual problem, more like concepts. What exactly is the dot product? How about the cross product?
  3. MathematicalPhysicist

    Understanding Cross Sections and Lifetimes: Questions 3 and 4

    Homework Statement In the attached file, I need some help with questions 3 and 4. Homework Equations The Attempt at a Solution For question 4, I get the next answers: a. The flux is given by: f=\frac{v_{\nu}\rho}{m} where m is the mass of the iron nucleus, rho is the iron...
  4. H

    Determinant, dot product, and cross product

    I am reading through David Widder's Advanced Calculus and he abbreviates a determinant as: \left( \begin{array}{cccc} r_{1} \ s_{1} \ t_{1}\\ r_{2} \ s_{2} \ t_{2}\\ r_{3} \ s_{3} \ t_{3}\\ \end{array} \right) And refers to it by (rst). He then states...
  5. Shackleford

    Cross Product and Triple Scalar Product

    This isn't homework, but I worked this out to become more fluent with expressing these operations using sums, indices, etc. This is from my Vector Analysis course, and the professor said understanding this would make the rest of the course smooth sailing if I get all these concepts down. I'm...
  6. M

    Question regarding vector (cross) product

    Yo guys, I was wondering: Why does the cross product of two vectors produce a third vector which is perpendicular to both the original vectors? I've come across it in math and it's one of those things I've accepted... but I'm not quite sure why it happens.
  7. M

    Cross product and dot product of forces expressed as complex numbers

    Homework Statement I have came up with an example to illustrate my question. There is a rod, which can turn around p1. p1p2 = (-1+j) m p1p3 = (-3 + 3j) m p1p4 = (1 - j ) m F1 = (1+3j) N F3 = (-1 - 2j ) N F4 = unknown, orthogonal to the rod compute F2_n, orthogonal component of F2 to the...
  8. Z

    Volume by cross-section: ellipse and equilateral triangle cross sections?

    Volume by cross-section: ellipse and equilateral triangle cross sections?? Homework Statement The base of a solid is the region bounded by the ellipse 4x^2+9y^2=36. Find the volume of the solid given that cross sections perpendicular to the x-axis are: a) equilateral triangles b) squares...
  9. Z

    Volumn by cross sections - solving in terms of which axis confusion?

    Homework Statement I need to find the volume of the solid generated by revolving this region bounded by the curves about the x-axis. y = sqrt(x), x+y=6, y=1 Homework Equations The Attempt at a Solution I find the intersections of these curves I get: (1,1), (4,2)...
  10. X

    Vector Cross Product Homework: Find 3rd Vector Perpendicular to C & D

    Homework Statement C= B|A| + A|B| D= A|B|-B|A| C and D are orthogonal Find a third vector perpendicular to both C and D Homework Equations [AxB] = |A||B|sin(theta) The Attempt at a Solution I know that to find the answer I need to find the cross product of C and D. I have done...
  11. E

    Vector calculus: divergence of a cross product

    Homework Statement I need to prove the identity div (a x b) = b dot (curl a) - a dot (curl b) The Attempt at a Solution I've done the proof about 10 times now, and everytime I get the left hand of the identity equal to this: (all the d's are partial derivatives) d(a3b1)/dx -...
  12. D

    Connection between cross product and partial derivative

    Hi. I have been looking at differential forms, and that inspired me to consider a partial derivative as a ratio between cross products. Please tell me if the following makes sense. Say we have cartesian coordinates (x,y) and polar coordinates (\rho, \phi). I want to calculate...
  13. K

    Singularity in Rutherford cross section

    The Rutherford differential cross section \frac{d\sigma}{d\Omega} goes like cosec(\vartheta)^4 which means at \vartheta=0 the differential cross section is infinite, which is ok. My question is, given that the differential cross section is proportional to the probability per unit solid...
  14. C

    Why does the dot product use cosine?

    What is significance of the trig functions in both the cross and the dot product? I understand what the dot and cross products are, how they work, and what they give...but I don't understand why the dot product uses cosine and the cross product uses sine?
  15. E

    Elastic reactions, ratio of cross sections

    Hello everybody, I am having some troubles with this exercise. I have attached the text and the solutions to my post. My problem is, after I have coupled the angular momenta and used the CK coefficients like in (|\pi ^{+}p>=|1,1>|1/2, 1/2>=|3/2,3/2>) (pag.432) I don't understand what...
  16. T

    Dot product and cross product evaluation questions

    This question has a few parts. r = i + 2j + 3k s = 2i - 2j - 5k t = i - 3j - k Evaluate: a)(r.t)s - (s.t)r b)(r x s) x t. deduce that (r.t)s - (s.t)r = (r x s) x t can you prove this relative true for any three vectors a)(r.t)s - (s.t)r (r.t)s well I don't know...
  17. W

    Cross product of magnetic fields

    Is there any physical meaning to the cross product of two magnetic fields e.g. two fields generated in two different current loops?
  18. N

    Reactor Neutrons: Seeing Surface Area not Projected Cross Section?

    My professor told me that the neutrons in a reactor see the surface area of nuclei, and not the the projected cross section. That really doesn't make intuitive sense. Is he right?
  19. D

    Transverse loading with varing cross section

    i know that τ=VQ/(Ib) now I am looking for the maximum stress so i will find that at the point at the centre of the rectangle Q=A*\bar{y} A=0.5*d*b \bar{y}=0.25*d ===> Q=0.125d2b I=(b*d3)/12 τ=VQ/(Ib) τ=V*0.125d2b*12/((b2*d3) τ=1.5V/(bd) now d changes as a function...
  20. H

    Finding Volume by Cross Section Area

    I need to find the volume of this figure y=sinx, y=sinx + 2, x=4, x=-4 using the area of triangular cross sections. i don't really know where to start...how to find the formula for area of cross section etc. HELP!
  21. D

    Finding stress in non symetric cross section

    in a given shaft with a circular cross section, the radius changes linearly find the maximum shear stress i used T*r/J and since J is dependant on r^4, i found that the cross section with the smallest radius will feel the largest stress. find the angle of twist at the end of the...
  22. N

    Area of Triangle with Cross Product: Equation Variations

    Hello! I'm trying to understand how this formula: 1/2 magnitude of v × w (area of triangle) yields the same value no matter which 2 adjacent sides are chosen. How would you prove mathematically that this is the case?
  23. J

    Understanding Products in the Equation v^2 = u^2 + 2aS

    In the equation v^2 = u^2 + 2aS , What kind of products are v^2 , u^2 , and aS ? Cross product or dot product?
  24. D

    What Are the Shear Stress and Angle of Twist for a Steel Member Under Torque?

    A 3.5 m long steel member with a W310 x 143 cross- section is subjected to 4.5KNm torque. Knowing that G=77GPa, determine (a) the maximum shearing stress along the line a-a, (b) the maximum shearing stress along the line b-b, (c) the angle of twist...
  25. B

    Are the Vector Operators K1 and K2 Hermitian or Anti-Hermitian?

    A and B are two hermitian vector operators. K1=AXB, K2=AXB-BXA. Are K1 and K2 hermitian or anti-hermitian?
  26. Z

    Question about property of Cross Product

    Homework Statement Hello. I am relatively new to this subject please forgive my incompetence. Please correct me if I have misunderstandings. I understand that the cross product of two vectors (say A and B) in R3 is a vector that is orthogonal to both A and B. But how A x B be...
  27. D

    PLEASE HELP How to Cross Product Two 3x3 matrices

    How do I take the cross product of Two 3x3 Matrices. For example what is cross product of: [-1 0 0] [0 1 0] [0 0 1] x [0 -1 0] [1 0 0] [0 0 1] thanks, Della
  28. W

    What Are Dot Products and Vector Cross Products in Mathematics?

    Can someone explain to me what a dot product and vector product of two vectors are? Be as detailed as possible please! And also why does the right hand rule for vectors work?
  29. J

    Cross hanging from rearview mirror

    A race-car driver is driving in a circle at a fixed velocity. He has a cross hanging down from a string on his rearview mirror. Which of the listed forces impacts the hanging cross as the driver drives around a circle at a fixed velocity? Gravity, Friction, Tension, and Centripetal Force I...
  30. A

    Find angle to eliminate cross product term

    Homework Statement If you make the change of variables: x= ucos(\theta)-vsin(\theta) y= usin(\theta)+vcos(\theta) where the angle 0 \leq \theta <\pi/2 is chosen in order to eliminate the cross product term in: 4x2+8xy+6y2=30 What is the angle you would use? Homework Equations...
  31. K

    Cross section for two identical particles in the final state

    I was calculating the cross section for a particular decay and saw that I was off by a factor of half from the known value.. Now, the decay has two identical particles in the final state and I seem to remember having read somewhere that this requires a factor of half...but I am not able to...
  32. D

    Relationship of Power and cross sectional area to electric field

    I am having difficulty finding the equation or relationship between power (watts) and cross sectional area (m2) to finding the value of an electric field. I am just confused and can't seem to understand and my textbook isn't making sense to me Any help would be appreciated and I...
  33. L

    What is the Cross Product and How Can I Understand It?

    I'm very confused by this cross product thing...help!
  34. L

    What is the correct angle between T and U in the cross product?

    1. Find the sine of the angle between and . 2. AxB = ABsin(alpha) 3. I know T = (3,1,0) and U = (2,4,0), and I calculated that V = TxU = (0,0,10), so the magnitude of V is 10. Then I did 10 = sqrt(10)*sqrt(20)*sin(alpha) Divided 10 by sqrt(10)*sqrt(20), took the inverse...
  35. R

    Cross product and the angles of a prallelogram

    Cross product and the angles of a prallelogram's diameters Homework Statement With the help of cross product prove: if the angle between the diameters of a parallelogram is 90 degrees, then the parallelogram is a rectangular. Homework Equations A\timesB=(surface of the parallelogram)...
  36. W

    Need help with combination of dot product and cross product question

    Homework Statement Let \vec{A}, \vec{B}, and \vec{C} be three vectors which are all not in the same plane. Show that \vec{A}{\cdot}(\vec{B}{\times}\vec{C})=\vec{B}{\cdot}(\vec{C}{\times}\vec{A})=\vec{C}{\cdot}(\vec{A}{\times}\vec{B}) Homework Equations Don't know :( The Attempt at...
  37. B

    Question regarding Curl and Cross Product

    I'm studying vector calculus, and have a question about the curl and its relation to a cross product of the del operator and a vector. When doing a standard cross product as the formula I have i(det1) - j(det2) + k(det3), where det1, 2 3 are the appropriate 2x2 determinants. However for the...
  38. C

    Another volume by cross section.

    The base of a solid is the triangular region bounded by the y-axis and the lines x + 2y = 4, x - 2y =4. Find the volume of the solid given that the cross sections perpendicular to the x-axis are isosceles right triangles with hypotenuse on the xy-plane. So what I did is: 2\int_{x=0}^2...
  39. naima

    Why does the amplitude <p |T| p'> have the dimension of a volume?

    Hello I am reading this book: "[URL and the appearance of a classical word&f=false"]decoherence[/URL] I hope someone could help me. Please go to Appendix A1 Joos introduces the notation f(q,q'). What is the dimension of f from his notation? Next page he writes that \int f^2 d\Omega...
  40. I

    How to Prove the Sine Rule Using Cross Product?

    Could anyone tell me how to use the cross product to prove the sine rule
  41. N

    Exploring the Defined & Used Form of the Cross Product

    Why is the cross product defined this way (blah)i + (blah)j + (blah)k = u and used this way (blah)i - (blah)j + (blah)k = u
  42. V

    Thermal Cross Sections: Find Info on Boric Acid, O2, Uranium, Water, etc.

    Where can I get reliable information on the cross section of various substances: boric acid, O2, Uranium, water, etc?
  43. T

    Dot product and cross product problem

    I am having problems with this questions my physics teacher gave us. Since he doesn't explain things well, I do not know how he got an answer of 66. Can you please explain to me how to get this answer? THX. For the following three vectors, what is C*(A X 3B) (the "*" is suppose to be a dot)...
  44. X

    What is the Geometric Interpretation of Dot and Cross Products?

    Describe the surface defined by the equation: (a) \vec{r}\cdot \hat{x}= 2, where \vec{r}=x\hat{x}+y\hat{y}+z\hat{z}; (b) \left \| \vec{r} \times \hat{x}\right \|=2 For the first one, I know that is interpreted as the projection of the r vector onto the x-axis is equal to two...
  45. L

    Cross Product Confusion: Solving UxV

    I was reading div grad curl and all that. Couldn't get something basic - cross product. U = iux + k df/dx (ux) V = jvy + k df/dy (vy) UxV = [ -i df/dx - j df/dy + k] uxvy can't figure out how to get U x V.
  46. H

    Showing that three points are collinear if their cross product is zero

    Homework Statement show that three points P,Q, and R are collinear if and only if vec PQ x vec PR = 0 Homework Equations The Attempt at a Solution i understand this (i can see this visually in my head) but i just don't know how to say it mathematically...i know that the angle...
  47. G

    Cross product of row and column vector

    For the two matrices A and B, (AB)i,j = ri . dj ---- . refers to dot product ---- ri is the ith row in A and dj is the jth column in B. Let us say that A and B are n x n system of column vectors. Then a row vector ri of A would correlate to a component vector of the sum of the column vectors...
  48. O

    How can div (u cross v) be proved using the product rule?

    Please show me the way the proof this! div (u cross v) = v dot grad (u)- u dot grad(v) where v and u is a vector. The product rule doesn't seem working
  49. G

    Infinite cross section in scattering

    Hi For example in e-e- -> e-e- scattering (electron-electron scattering) the differential cross section goes to infinity as theta goes to zero. Consequently the cross section is infinite. But how can we measure and interpret the cross section/differential cross section and interpret it as a...
  50. C

    Understanding Cross Product: A Refresher for 3(A x B) Calculation

    Homework Statement I simply forget how to cross product if you have: 3(A x B) Would it be 3A x B or A x B then take that result and multiply by 3?
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