Vector Definition and 1000 Threads

  1. Mzzed

    I Method for solving gradient of a vector

    I have seen two main different methods for finding the gradient of a vector from various websites but I'm not sure which one I should use or if the two are equivalent... The first method involves multiplying the gradient vector (del) by the vector in question to form a matrix. I believe the...
  2. Curiose

    So, is my approach for finding angles efficient and accurate?

    For one of my current projects in computer vision (which really is a study in point clustering and tracking in a data stream of n-dimensional data), I have come up with a way to very quickly index a 2D angle between two points or the angle of a vector. Doing a little bit of investigation, and...
  3. V

    Vector problem -- Find the angle between vector A and vector B

    Homework Statement Vector A + Vector B + Vector C = 0 A=B+C Homework Equations Find the angle between vector A and vector B The Attempt at a Solution I tried to solve this problem by resolving all the vectors and individually equating the value of vectors at each axes x, y and z to 0 but got...
  4. P

    Poynting vector of current carrying wire

    Homework Statement A long straight wire of radius a and resistance per unit length R carries a constant current I. Find the Poynting vector N = E × H at the surface of the wire and give a sketch showing the directions of the current, the electric field E, the magnetic field H, and N. Integrate...
  5. S

    Finding the velocity of flow described by a vector field

    Homework Statement Consider the surface, S, in the xyz-space with the parametric representation: S: (, ) = [cos() , sin() , ] −1/2 ≤ ≤ 1/2 0 ≤ ≤ os(). The surface is placed in a fluid with the...
  6. T

    Perceptron algorithm initial vector

    In a scientific paper (Neural Networks: A Systematic Introduction, page 86) about the Perceptron Algorithm I found: A good initial heuristic is to start with the average of the positive input vectors minus the average of the negative input vectors. In many cases this yields an initial vector...
  7. L

    I with this question about vectors

    Homework Statement At noon two boats P and Q have a position vector (i+7j)km and (3i+8j)km respectively to the origin O. i and j are unit vectors in direction to East and north respectively P is moving south east at 5√2 km/h and Q is moving at a constant velocity of (6i+5j) km/h At time t after...
  8. Pushoam

    Calculating angle between velocity and position vector

    Homework Statement Homework EquationsThe Attempt at a Solution I took ## \frac { d\vec r}{dt} = 0 ## . This gives ##t_m = \frac { 1} {\sqrt{ 2}} ## ...(1) To calculate ## \alpha ## , ## \cos{ \alpha } = \frac { \vec v \cdot \vec r}{|\vec v||\vec r|} ## ...(2) Then, magnitude of...
  9. L

    Vector Subtract Given Magnitude

    Homework Statement Let's say i was given Vector A and B. The Angle between them is 60 degrees. Vector A's magnitude is 40 and Vector B's magnitude is 50. Find magnitude of vector C, if C = vector A - vector B. Homework Equations I'm given the magnitudes, and need to find magnitude of C The...
  10. S

    Graphics illustrating vector potential for plane EM wave

    I'm looking for a diagram or animation that shows the vector potential A (in the form of arrows or whatever) superimposed on the E and B fields of a plane EM wave. Since A is not unique, maybe two or three versions of the diagram (including one with Coulomb guage). An animation with a slider to...
  11. binbagsss

    QFT T-duality, Massless vector states

    Homework Statement Part C) Please: Homework Equations above,below The Attempt at a Solution so I think I understand the background of these expressions well enough, very briefly, changing the manifold from ## R^n ## to a cylindrical one- ##R^{(n-1)}^{+1}## we need to cater for winding...
  12. allison west

    Vector Potential of a Rotating Mangetic Dipole

    Homework Statement A rotating magnetic dipole is built by two oscillating magnetic dipole moments, one along the y-axis and one along the x-axis. Find the vector potential at a point: (0, 0, ##z_0##) along the z-axis. Then find the magnetic field at ##z_0## . As the magnetic field is a function...
  13. I like Serena

    MHB What is the basis of the trivial vector space {0}

    It makes me wonder... wikipedia says about a basis: In mathematics, a set of elements (vectors) in a vector space V is called a basis, or a set of basis vectors, if the vectors are linearly independent and every vector in the vector space is a linear combination of this set.[1] So what is the...
  14. hzx

    Crystallography; from hcp to fcc

    Homework Statement Three close-packed planes of atoms are stacked to form fcc lattice. The stacking sequence of the three planes can be altered to form the hexagonal close packed structure by sliding the third plane by the vector r over the second. If the planes in the fcc structure are all...
  15. T

    Calculate the Curl of a Velocity vector field

    Homework Statement The velocity of a solid object rotating about an axis is a field \bar{v} (x,y,z) Show that \bar{\bigtriangledown }\times \bar{v} = 2\,\bar{\omega }, where \bar{\omega } is the angular velocity. Homework Equations 3. The Attempt at a Solution [/B] I tried to use the...
  16. yecko

    Understanding Flux of Vector Fields: Equations, Solutions, and Common Mistakes

    Homework Statement Example 2:[/B] Homework Equations Flux=integrate -Pgx-Qgy+R of the proj. area on xy plane for z=g(x,y) The Attempt at a Solution Why do my attempt is wrong? The example is using the foundational formula while I use the stock formula from the book, why is there a negative...
  17. E

    Vector fields question; not sure how to approach?

    Homework Statement The stream function Ψ(x,y) = Asin(πnx)*sin(πmy) where m and n are consitive integers and A is a constant, describes circular flow in the region R = {(x,y): 0≤x≤1, 0≤y≤1 }. Graph several streamlines with A=10 and m=n=1 and describe the flow. Explain why the flow is confined to...
  18. yecko

    Line integral of a vector field

    Homework Statement [/B] I would like to ask for Q5b function G & H Homework Equations answer: G: -2pi H: 0 by drawing the vector field The Attempt at a Solution the solution is like: by drawing the vector field, vector field of function G is always tangential to the circle in clockwise...
  19. D

    How to prove vector identities WITHOUT using levi civita ?

    Mentor note: Thread moved from homework sections as being a better fit in the math technical section. Multiplying components of both sides are also off limits. I am trying to derive vector identities on introduction chapters in various EMT books. For example : (AXB).(CXD) = (A.C)(B.D) -...
  20. J

    I Definition of Vector Field in General Relativity

    In general relativity we demand that the physical law can be stated as a form which does not depend on the choose of particular coordinate system, So the vector field is defined as a changing object following a regular pattern under the transformation of coordinates. For example, we can define...
  21. binbagsss

    GR: find covariantly constant vector on a given curve

    Homework Statement I am stuck on finding ##W^u## Homework Equations [/B] I have computed the christoffel symbols via comparing the Euler-Lagrange equations to the form expected from geodesic equation. geodesic equation: ##\ddot{x^a}+\Gamma^a_{bc}\dot{x^b}\dot{x^c}=0## covariantly constant...
  22. binbagsss

    GR timelike vector show properties/decomposition holds

    Homework Statement Homework Equations above The Attempt at a Solution I'm totally stuck as to how to get to started , how to use the hint to decompose a vector given a preferred spacetime direction. All I know is that any tensor can be decomposed into a anti symmetric and a symmetric...
  23. Alexander350

    B Solving a differential equation with a unit vector in it

    I need to solve: \dot{\mathbf{r}}=-kv\hat{r} - \dot{\mathbf{r}_s} However, I do not know how to deal with the fact that there is a unit vector. How can this be done? \dot{\mathbf{r}_s} is a constant vector.
  24. Y

    I What does this vector notation mean?

    Hello, I'm currently doing vectors in class, but I don't know what these parts mean. Especially φ(a,b). I understand cos(φ), but I don't understand cos(φ(a,b)). φ is the angle between two vectors a and b, but what does the (a,b) part add? I tried to google, but I couldn't really find...
  25. R

    Find a basis for R2 that includes the vector (1,2)

    My answer was [ (1,2), (0,-1) ] I just wanted to make sure with you guys that you could essentially have an infinite amount of answers. For example: [ (1,2), (0,1) ] [ (1,2), (0, -5) ] etc would all suffice, right?
  26. S

    Cylindrical Vector Field Equation Convsersion to Cartesian

    Homework Statement I have been given a changing magnetic field in cylindrical coordinates. The equation is: \begin{equation} B(r,\phi,z) = - \frac {B_1} {2} r \hat{r} + (B_0 + B_1z)\hat{z} \end{equation} I need to be able to find the magnetic field as a function of x, y, and z. Homework...
  27. Kara386

    I Define inner product of vector fields EM

    I'm reading a textbook on electromagnetism. It says that for two vector fields ##\textbf{F}(\textbf{r})## and ##\textbf{G}(\textbf{r})## their inner product is defined as ##(\textbf{F},\textbf{G}) = \int \textbf{F}^{*}\cdot \textbf{G} \thinspace d^3\textbf{r}## And that if ##\textbf{F}## is...
  28. J

    I Choosing points from a set that produce the largest polygon

    I am trying to find the most efficient way to select points on a 2d plane from a set that maximizes the area of the of the shape they define when joined together. The points are all paired (sharing the same A->B vector), with these pairs also appearing mirrored about the origin. Here is an...
  29. Math Amateur

    MHB The Directional Derivative .... in Scalar Fields and Vector Fields ....

    I need some guidance regarding the directional derivative ... Two books I am reading introduce the directional derivative somewhat differently ... these books are as follows: Theodore Shifrin: Multivariable Mathematics and Susan Jane Colley: Vector Calculus (Second Edition)Colley...
  30. M

    Vector Form: Line Passing Through (2, -1) and Parallel to 2x-3y=1

    Homework Statement Find the vector form of the equation of the line in ℝ2 that passes through P=(2, -1) and is parallel to the line with general equation 2x-3y=1. Homework Equations None. The Attempt at a Solution vector form: x=p+td general form: ax+by=c --------------------------------...
  31. Math Amateur

    MHB How Does Definition 8.9 Imply Differentiability Near Point p?

    I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 8: Differentiable Maps and am specifically focused on Section 8.2 Differentials ... I need help in fully understanding Browder's comments on Definition 8.9 ... ... Definition...
  32. Math Amateur

    MHB Differentiation of Vector Valued Functions - Browder, Proposition 8.12 ....

    I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 8: Differentiable Maps and am specifically focused on Section 8.2 Differentials ... I need help in proving Proposition 8.12 ... ... Proposition 8.12 and the definitions...
  33. Math Amateur

    MHB Reconciling Differences in Vector-Valued Function Derivatives

    I am trying to reconcile apparent differences between the definitions of the derivative of a vector-valued function f: U \rightarrow \mathbb{R}^n (where U \subset \mathbb{R}^m ) of a vector variable from two textbooks ... The textbooks are as follows: Andrew Browder: "Mathematical Analysis...
  34. R

    Can F_1,2 Be Defined Using r-hat_2,1 Instead of r-hat_1,2?

    In this example (https://imgur.com/a/pTFIt) could i define F_1,2 in terms of r-hat_2,1 instead of r-hat_1,2?
  35. EastWindBreaks

    What is the direction of P relative to A?

    Homework Statement Homework Equations The Attempt at a Solution does Vpa has the same direction as Vp? i thought Vp is tangent to the circular path that point P creates( perpendicular to vector Rpa) but from the figure, Vp doesn't seem to be tangent to the path, but Vpa does...
  36. Y

    I How does the Vector Laplacian come about?

    So the Laplacian of a scalar is divergence of the gradient of a scalar field, and it comes out to the double derivative of the field in X, Y, and Z. My book says the Laplacian of a vector field is the double derivative of the X component of the field with respect to X, the double derivative of...
  37. B

    Waves and Vibrations -- Vector Diagram

    Homework Statement A lightly damped oscillator (mass, m, and spring constant,s, damping constant, b, with one end fixed) under external harmonic force (F0cosωt).(i.e., Standard mass-spring system with lubricated damper, and driven by an external harmonic force.) Since it is lightly...
  38. DoobleD

    When does the vector potential A affect the E field?

    This is probably fairly simple, but I have a hard time to grasp the concept of the vector potential A in electromgnetism. Especially, in the following equation for the electric field : \vec{E} = - \nabla V - \frac{\partial \vec{A}}{\partial t} When does the second term is not 0 ?
  39. S

    How Do You Calculate Velocity and Acceleration from a Position Vector?

    Homework Statement The position vector of an object of mass 0.10 kg at time t in seconds is given by =(^3+5)−4+2^2 Find the velocity and the acceleration as a function of t Homework Equations =(^3+5)−4+2^2 The Attempt at a Solution For velocity I think the equation needs to be...
  40. M

    Calculating the velocity and acceleration given vector velocity at 1 second

    Homework Statement A physics student studying gravity on the surface of Mars, throws a ball into the air at time t=0s. The ball follows a parabolic trajectory as shown and reaches a maximum height height at t=2s. At t=1s the velocity of the ball is v(t=1s)= 2.00 m/s i + 3.72 m/s j where i and j...
  41. S

    Find the basis of a vector subspace of R^2,2

    Homework Statement i know how to find the basis of a subspace of R2 or R3 but I can't figure out how to find the basis of a subspace of something like R2,2. I even have an example in my book which i managed to follow nearly till the end but not quite... Given matrix: A= 6 -9 4 -4 show that...
  42. M

    Question about Finding a Force with line integrals

    Homework Statement [/B] F =< 2x, e^y + z cos y,sin y > (a) Find the work done by the force in moving a particle from P(1, 0, 1) to Q(1, 2, −3) along a straight path. (b) Find the work done by the force in moving a particle from P(1, 0, 1) to Q(1, 2, −3) along the curved path given by C : r(t)...
  43. yecko

    Derivative of directional vector

    Homework Statement Find the unit vectors along which the given functions below increase and decrease most rapidly at P0 . Then find the derivatives of the functions in these directions. Homework Equations solution: The Attempt at a Solution why are the derivatives’ values along these...
  44. A

    I Relativistic Mass Calculation with 4th Dimensional Vector

    I have a sample problem : Photon, with energy E, is absorbed by m. Then, mass m becomes m' (i think it's relativistic mass). Calculate the new mass. My teacher solved the problem as follows; P1=( E/c, P3dphoton); // momentum of the photon P2=(mc, 0); // momentum of the stationary mass...
  45. M

    Question about Vector Fields and Line Integrals

    Homework Statement (a) Consider the line integral I = The integral of Fdr along the curve C i) Suppose that the length of the path C is L. What is the value of I if the vector field F is normal to C at every point of C? ii) What is the value of I if the vector field F is is a unit vector...
  46. N

    How do i choose the Surface area vector in different cases?

    Homework Statement Suppose we have a Electic field, E (vector) = kr2r(vector). Find the total charge contained in the sphere of radius R centered in the origin. solution- here E can also be written as kr3r∧, where r∧ is the unit vector this is the given question , so obiously the best way to...
  47. L

    Finding distance of "P" from a plane OQR using vector

    Homework Statement Find th distance of point P to the plane OQR, O being the origin. "PS" is perpendicular to plane "OQR" P(3,-2,-1) S(x,y,z) O(0,0,0) Q(1,3,4) R(2,1,-2) Homework Equations A) The equation in terms of (x,y,z) obtain by triple product of OS,OQ & OR. OS.(OQXOR)=0... [all being...
  48. karush

    MHB Calculate Vector Integral $\vec{V_2}$

    \begin{align*}\displaystyle \vec{V_2} &=\int_0^3 \left[\left( \frac{4}{\sqrt{1+t}}\right){I}-\left(7t^2 \right){j} +\left(\frac{14t}{\left(1+t^2 \right)^2}\right){k}\right] dt \\ &=\left[\int_0^3 \frac{4}{\sqrt{1+t}} dt \right] {I} -\left[\int_0^3 7t^2 dt\right] {j} +\left[...
  49. Philosophaie

    I Partial Vector Derivative: Is This the Correct Derivative of B?

    Is this the correct partial derivative of B? ##\vec{B} = \frac{g \vec{r}}{4 \pi r^3}## ##\frac{\partial \vec B}{\partial r}## = ##-3\frac{g \vec{r}}{4 \pi r^4} + \frac{g}{4 \pi r^3 }(\frac{\partial r_r \hat r}{\partial r})##
  50. 1

    The Divergence of a Regularized Point Charge Electric Field

    1. Problem: Consider vector field A##\left( \vec r \right) = \frac {\vec n} {(r^2+a^2)}## representing the electric field of a point charge, however, regularized by adding a in the denominator. Here ##\vec n = \frac {\vec r} r##. Calculate the divergence of this vector field. Show that in the...
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