Vector Definition and 1000 Threads

  1. F

    I Factors for contravariant components with transported vector

    I am currently coding a small application that reproduces the transport of a vector along a geodesic on a 2D sphere. Here's a capture of this application : You can see as pink vectors the vectors of curvilinear coordinates and in cyan the transported vector. The transport of vector along...
  2. S

    Verifying Subspace of P3: Closure of Addition & Scalar Multiplication

    Homework Statement Determine if the following is a subspace of ##P_3##. All polynomials ##a_0+a_1x+a_2x^2+a_3x^3## for which ##a_0+a_1+a_2+a_3=0## Homework Equations use closure of addition and scalar multiplication The Attempt at a Solution Let ##P=a_0+a_1x+a_2x^2+a_3x^3## and...
  3. A

    Vector Proof Homework: The Rotation Matrix

    Homework Statement Homework Equations The Rotation Matrix The Attempt at a Solution I am sorry but I do not know how to even begin
  4. Prof. 27

    Angle between vector and tangent vector

    Homework Statement My problem is: For the logarithmic spiral R(t) = (e^t cost, e^t sint), show that the angle between R(t) and the tangent vector at R(t) is independent of t. Homework Equations N/A The Attempt at a Solution The tangent vector is just the vector that you get when you take the...
  5. H

    Intrinsic derivative of constant vector field along a curve

    Homework Statement Suppose that ##T_i## is the contravariant component of a vector field ##\mathbf{T}## that is constant along the trajectory ##\gamma.## Show that intrinsic derivative is ##0.## Homework Equations $$\frac{\delta T_i}{\delta t} = \frac{dT^i}{dt}+V^j\Gamma^i_{jk}T^k$$ The...
  6. F

    I Understanding Separable Vector Spaces: The Basics Explained

    Dear forum, I am trying to understand what a separable vector space is. I know we can perform the tensor product of two or more vector space and obtain a new vector space. Is that vector space separable because it is the product of other vector spaces? thanks
  7. F

    I Notations used with vector field and dot product

    Hello, I try to understand the following demonstration of an author (to proove that dot product is conserved with parallel transport) : ------------------------------------------------------------------------------------------------------------------------ Demonstration : By definition, the...
  8. B

    Calculating Distance and Displacement in Vector Problems

    Homework Statement Darryl drives his load of tomatoes 14.0 km [E], 6.0 km [N], 12.0 km [N 15° E], and then 2.0 km [N 65° E]. This takes him 42 minutes. Calculate Darryl’s distance and displacement. Then draw a diagram to show your work. [/B]Homework Equations Not really sure.[/B]The Attempt...
  9. A

    X and Y components of a vector using a graph of speed/time

    Homework Statement A golf ball is struck at ground level. The speed of the golf ball as a function of the time is shown in the figure, where t = 0 at the instant the ball is struck. The scaling on the vertical axis is set by va= 16 m/s and vb= 29.3 m/s. (a) How far does the golf ball travel...
  10. S

    A Understanding Vector Mass in Particle Physics Models

    I hear the phrase vector mass being used a lot in discussions of various models in particle physics. But I am not exactly sure what it means. There is no Wikipedia article on this term. Is vector mass somehow different from scalar mass? The only possible mass terms in the Lagrangian arise due...
  11. Jarvis88

    Introductory Vector Problem- Airplane emergency landing

    Homework Statement [/B] A plane leaves the airport in Galisteo and flies 180 km at 67.0 degrees east of north; then it changes direction to fly 255 km at 49.0 degrees south of east, after which it makes an immediate emergency landing in a pasture. When the airport sends out a rescue crew, how...
  12. M

    MHB Is $\Phi|_{U_2}$ a Vector Space Isomorphism?

    Hey! :o Let $V$ be the real vector space $\mathbb{R}[X]$ and $M \subset \mathbb{R}$ a set with $d$ elements. Let $$U_1 := \{ f \in \mathbb{R}[X] | \forall m \in M : f(m) = 0\}, \ \ U_2 := \{ f \in \mathbb{R}[X] \mid \deg(f) \leq d − 1\}$$ be two vector spaces of $V$. Let $\Phi: V\rightarrow...
  13. E

    Sparsity of Support vector machines over an RKHS

    Im trying to solve the following problem from the book 'Learning with kernels', and would really appreciate a little help. Background information - Let $\{(x_{1},y_{1}),...,(x_{N},y_{N})\}$ be a dataset, L a Loss function and $H(k)$ a reproducing kernel Hilbert space with kernel $k$. The...
  14. Kaura

    Solve for Path of Particle: x - 2cos(arcsin(y/2)) = 0

    Homework Statement Suppose that a particle follows the path r(t) = 2cos(t)i + 2sin(t)j Give an equation (in the form of a formula involving x and y set equal to 0 ) whose whose solutions consist of the path of the particle. Homework Equations None that come to mind The Attempt at a Solution I...
  15. M

    I How is a vector a directional derivative?

    I'm going through a basic introduction to tensors, specifically https://web2.ph.utexas.edu/~jcfeng/notes/Tensors_Poor_Man.pdf and I'm confused by the author when he defines vectors as directional derivatives at the bottom of page 3. He defines a simple example in which ƒ(x^j) = x^1 and then...
  16. enerieire

    How Is the Flux of Poynting's Vector Calculated Through a Surface?

    I have some problems in calculating the flux of Poynting's vector through a surface. I have that: S=c/4π⋅H^2⋅n (S: Poynting's vector, n: versor of the direction of the propagation of the em wave) H=1/cR A' but: A=(1/cR) d'; A'=(1/cR) d'' ==> H= (1/cR)^2 d''...
  17. rumborak

    I How does the Poynting vector factor into a normal circuit?

    So, the Wiki page on the Poynting vector has this image: I remember hearing/reading somewhere that the energy transmission in a circuit like this is actually not traveling through the wire, but that it actually happens through the electromagnetic field, I.e. essentially the Poynting vectors...
  18. Alettix

    Point inside a tetrahedron with vectors

    Homework Statement As part of a longer problem: "Find necessary and sufficient conditions for the point with positionvector r to lie inside, or on, the tetrahedron formed by the vertices 0, a, b and c." Homework Equations I am not sure... vector addtion? The Attempt at a Solution I don't...
  19. B

    Statics: Dimensionless Unit Vector

    Homework Statement Homework Equations The Attempt at a Solution So I began by subtracting. (205-160)=55 i (495+128)=623 j Both of these vectors are in the positive direction. So if I divide the vector by its magnitude I should get an answer of 1 in the positive direction for both i and...
  20. ubergewehr273

    B Confusion between ##\theta## and ##d\theta##

    Why is ##\theta## a scalar whereas ##d\theta## a vector ?
  21. L

    Divergence theorem for vector functions

    Surface S and 3D space E both satisfy divergence theorem conditions. Function f is scalar with continuous partials. I must prove Double integral of f DS in normal direction = triple integral gradient f times dV Surface S is not defined by a picture nor with an equation. Help me. I don't...
  22. BubblesAreUs

    Determine whether the subset is a vector subspace

    Homework Statement Recall that F is the vector space of functions from ℝ to ℝ, with the usual operations of addition and scalar multiplication of functions. For each of the following subsets of F, write down two functions that belong to the subset, and determine whether or not the subset is a...
  23. M

    Proving Linear Independence of Av1, ..., Avk and Conditions for Basis in Rm

    Homework Statement [/B] 1. Suppose {v1, . . . , vk} is a linearly independent set of vectors in Rn and suppose A is an m × n matrix such that Nul A = {0}. (a) Prove that {Av1, . . . , Avk} is linearly independent. (b) Suppose that {v1, . . . , vk} is actually a basis for Rn. Under what...
  24. Q

    I Christoffel Symbol vs. Vector Potential

    As far as I can tell, in GR, the Chirstoffel symbol in the expression of the Connection is analogous to the vector potential, A, in the definition of the Covariant Derivative. The Chirstoffel symbol compensates for changes in curvature and helps define what it means for a tensor to remain...
  25. A

    Why does (ax, by) not transform like a vector under rotation?

    Homework Statement Show that (ap1,bp2) is not a vector unless a = b.(The 1 and 2 are superscripts) In Einstien's Gravity in a Nutshell, p 43, Zee states the above is not a vector because it doesn't transform like a vector under rotation. When I use the usual rotation matrix for rotation about...
  26. M

    A Why are open strings vectors or scalars, or massive?

    In string theory, if we have NN BCs along ##X^i, i = 1, \ldots, n-1## and DD BCs along ##X^a, a = n, \ldots, 25## then you get, from ##\alpha^{i,a}_{-1}|0,p\rangle ##, ##n## massless vectors and ##24-n## massless scalars. I understand that for the first excited level, ##M^2=0## and so we have...
  27. F

    I Basis of a Subspace of a Vector Space

    Hello Forum and happy new year, Aside from a rigorous definitions, a linear vector space contains an infinity of elements called vectors that must obey certain rules. Based on the dimension ##N## (finite or infinite) of the vector space, we can always find a set of ##n=N## linearly independent...
  28. karush

    MHB S6.194.4.12.4.29 Find a nonzero vector orthogonal to plane

    $\tiny{s6.194.4.12.4.29}$ $\textsf{a. Find a nonzero vector orthogonal to plane through the points: }$ $\textsf{b. Find the area of the triangle PQR}$ \begin{align} \displaystyle &P(1,0,0)& &Q(0,2,0)& &R(0,0,3)\\ %&=\color{red}{\frac{1209}{28} } \end{align} $\textit{do what first?}$
  29. F

    I State Representation in QM and Vector Spaces

    Hello Forum, The state of a quantum system is indicated by##\Psi## in Dirac notation. Every observable (position, momentum, energy, angular momentum, spin, etc.) corresponds to a linear operator that acts on ##\Psi##.Every operator has its own set of eigenstates which form an orthonormal basis...
  30. cathal84

    Finding length of vector with unknown variable

    Finding length of vector with unknown variable. Purely for study purposes. Find the smallest possible length of the vector →v . Let vector V = (-2/3,b,16/7) Equation for finding length of vector : Sqrt(a^2+b^2+c^2)Question would be quite straight forward had there been no unknown variable but...
  31. P

    B Is Center of Mass a vector or scalar quantity?

    I am a little bit confused on Center of Mass and Center of Gravity about what are they vectors or scalars . As I may think they are neither because they are simply two points . Am I saying right or wrong .
  32. T

    I Multiplying a vector by a complex number

    I have learned that if I multiply a vector, say 3i + 4j, by a scalar that is a real number, say 2, the effect of the operation is to expand the size of the magnitude of the original vector, by 2 in this case, and the result would be 6i + 8j. What would be the effect on a vector, like 3i + 4j...
  33. redtree

    I Fourier transform of the components of a vector

    Given the Fourier conjugates ##\vec{r}## and ##\vec{k}## where ##\vec{r} = [r_1,r_2,r_3]## and ##\vec{k} = [k_1,k_2,k_3]## , are ##r_1## /##k_1##, ##r_2##/##k_2##, ##r_3##/##k_3## also Fourier conjugates, such that: ##\begin{equation} \begin{split} f(\vec{r})&=[f_1(r_1),f_2(r_2),f_3(r_3)] \\...
  34. Muhammad Khalid Khan

    Total displacement using vector diagram

    A car is driven eastward for a distance of 50 miles, then northward for 30 miles, and then in a direction 30 degree east of north for 25 miles. Draw the vector diagram and determine the total displacement of the car from its starting point. The relevant equations I used here are: i) rx= ax +...
  35. H

    Finding ez: Solving a 3D Vector Equation

    Homework Statement Find the value of ez if e = 1/3i + 2/3j + ezk Homework Equations Any help? The Attempt at a Solution Have no idea where to start
  36. williamwong0402

    How Do You Calculate Force in Vector Form?

    Hi everyone please help how can i find the force in Q(a)(ii)?
  37. L

    MHB Solve Vector Space Question: Get the Solution Now

    How do you solve this question I just need a solution
  38. M

    Vector Calculus - Tensor Identity Problem

    Homework Statement Homework Equations The Attempt at a Solution I am really lost here because our professor gave us no example problems leading up to the final exam and now we are expected to understand everything about vector calculus. This is my attempt at the cross product and...
  39. doktorwho

    Velocity vector and velocity intensity

    Homework Statement Given the velocity vector in the polar coordinates, ##\vec v=-awsin{wt}\vec e_r + awcos{wt}\vec e_\theta## determine the average velocity vector and velocity intensity over a time period ##[0, \pi/2w]## Homework Equations 3. The Attempt at a Solution [/B] For the first part...
  40. S

    Angle between vector and z-axis

    1. Homework Statement I am looking at problem 2.2 pictured above. I have solved all portions of the question except the last part, which asks for the angle between the normal vector to the surface and the z-axis. I am aware that the normal vector is simply equal to the gradient of the surface...
  41. B

    What is the Direction of A X B Using the Right Hand Rule?

    Homework Statement The direction of vectors A and B are given below for several cases. For each case, state the direction of A X B. a) A points east, B points south. b) A points east, B points straight down. c) A points straight up, B points north. d) A points straight up, B points straight...
  42. C

    Rate of Change of Vector in Rotating Frame

    I recognize the rate of change of a vector in an inertial frame S can be related to the rate of change of the vector in a rotating frame S0 by the equation below taken from my textbook, where Ω is the angular velocity vector. $$\Big(\frac{dQ}{dt}\Big)_{S_{0}}= \Big(\frac{dQ}{dt}\Big)_{S} +...
  43. maxhersch

    Estimate Vector Field Surface Integral

    I assume this is a simple summation of the normal components of the vector fields at the given points multiplied by dA which in this case would be 1/4. This is not being accepted as the correct answer. Not sure where I am going wrong. My textbook doesn't discuss estimating surface integrals...
  44. M

    MHB Are $V_1$ and $V_2$ Vector Spaces According to Defined Properties?

    Hey! :o I want to check if the following are true. $V_1=\{a\in \mathbb{R}\mid a>0\}$ with the common multiplication as the vector addition and the scalar multiplication $\lambda \odot v=v^{\lambda}$ is a $\mathbb{R}$-vector space. $V_2=\{(x,y)\in \mathbb{Q}^2 \mid x^2=-y^2\}$ with the...
  45. S

    I Vector Calculus: What do these terms mean?

    In our section on path independence, we were asked to find the potential function given a vector field. Our teacher says to use only line integrals to find the potential function, and not any other method. Like if we have ##F=\left< M,N,P \right> ## The first step is to determine if the domain...
  46. StudentOfScience

    Kleppner - Example 1.18: Representation of Position Vector

    Homework Statement Bead on spoke: constant speed ##u## along spoke it starts at center at ##t=0## angular position is given by ##\theta=\omega t##, where ##\omega## is a constant Homework Equations ## \frac{d\hat r}{dt} = \dot \theta \hat \theta ## (1) ## \frac{d\hat \theta}{dt} = -\dot...
  47. garylau

    What is the meaning of Ai Aii Bi Bii in Vector potential?

    Sorry may i ask a question here~ i don't understand how did GRIFFITHS prove the statement from(C) to (B) What is his logic in this case? and What is Ai Aii Bi Bii in the integral? thank you
  48. H

    Vector Nature pf Projectile Motion

    Homework Statement If an object had been projected horizontally with the same magnitude as in the depicted situation, how would the motion compare with that of the object in the diagram? (I have drawn the diagram in my attachment and have done questions c and d but I don't understand question...
  49. P

    Induced Magnetic Moment (vector) vs. Induced EMF (scalar)

    When I induce magnetic flux through a closed loop, I should expect the lines of flux produced by current in that loop to oppose the change of flux through that loop. But what happens when that loop, say a rectangular loop, is curved into the shape of the letter J (like a candy cane) and my flux...
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