Vector Definition and 1000 Threads

  1. babaliaris

    I Pendulum Tension Force -- How to calculate the full vector?

    Hello! I'm trying to understand how this pendulum works. I found this video that explains how to calculate the T force from the rope. He uses the preservation of kinetic and potential energy in order to find the magnitude of the velocity and then using Newton's second law, he calculates the T...
  2. P

    Evaluating the Integral of a Vector Field Using Cauchy-Schwarz Inequality

    Here is my attempt (Note: ## \left| \int_{C} f \left( z \right) \, dz \right| \leq \left| \int_C udx -vdy +ivdx +iudy \right|## ##= \left| \int_{C} \left( u+iv, -v +iu \right) \cdot \left(dx, dy \right) \right| ## Here I am going to surround the above expression with another set of...
  3. S

    Correct vector diagram of forces

    The answer is (B) but I don't understand why (C) is wrong. The force acting on the hinge has two components, horizontal and vertical. The horizontal component must be to the right to balance the horizontal component of tension but the vertical component can be either upwards or downwards. Wow to...
  4. tbn032

    B Confusion about the angle between two vectors in a cross product

    The magnitude of cross product is defined of vector A⃗ and B⃗ as |A⃗×B⃗|=|A⃗||B⃗|sinθ where θ is defined as the angle between the two vector and 0≤θ≤π.the domain of θ is defined 0≤θ≤π so that the value of sinθ remains positive and thus the value of the magnitude |A⃗||B⃗|sinθ also remain positive...
  5. K

    I Vector operator acting on a ket gives a ket out of the state space

    Definition of linear operator in quantum mechanics "A linear operator ##A## associates with every ket ##|\psi\rangle \in \mathcal{E}## another ket ##\left|\psi^{'}\right\rangle \in\mathcal{E}##, the correspondence being linear" We also have vector operators ##\hat{A}## (such as a position...
  6. S

    Is 2i + j + 3k the Normal Vector of Plane CDPQ?

    I know the normal of plane ABQP is -2i - j + 3k but I don't know how to prove that 2i + j + 3k is the normal vector of plane CDPQ Thanks
  7. patric44

    Confusion about four vector notation

    hi guys I am trying to learn special relativity and relativistic quantum mechanics on my own and just very confused about the different conventions used for the notation!?, e.g: the four position 4-vector some times denoted as $$ x_{\mu}=(ct,-\vec{r})\;\;or\;as\;x_{\mu}=(ict,\vec{r}) $$ or...
  8. Addez123

    Find surface of maximum flux given the vector field's potential

    The vectorfield is $$A = grad \Phi$$ $$A = x^2 + y^2 + z^2 - (x^4 + y^4 + z^4 + 2x^2y^2 + 2x^2z^2 + 2y^2z^2)$$ The surface with maximum flux is the same as the volume of maximum divergence, thus: $$div A = 6 - 20(x^2 + y^2 + z^2)$$ This would suggest at the point 0,0,0 the flux is at maximum...
  9. robphippen

    I Understanding Spin States in 2D Vector Spaces

    There is a passage in this book where I don't follow the logic; In this short quotation from 'Quantum Mechanics: The Theoretical Minimum' by Leonard Susskind and Art Friedman \mathcal{A} represents the apparatus that is performing the measurement the apparatus can be oriented (in principle) in...
  10. S

    Finding the position vector for translated frame of reference

    what would be the y'-x' ##\vec r## vector be? I think it is ##\vec r = (8t - 1) \hat i + (6t - 2) \hat j## (not sure whether it is correct or not.) I thought about it as at t = 0 the position needs to be -1i -2j so that is why I took the signs in the y'-x' frame position vector as a - instead...
  11. arjun_ar

    Calculate the magnetic field from the vector potential

    I am trying to derive radial and axial magnetic fields of a current carrying loop from its magnetic vector potential. So far, I have succeeded in deriving the radial field but axial field derivation gives me trouble. My derivation of radial field (eq 1) can be found here. Can anyone point out...
  12. hjam24

    Determine vertical velocity vector on sloped surface

    A golf is launched at a speed v,f and launch angle, β,f. The slope of the green is equal to φ. At some point the ball is located on the rim of a hole. The side view (a) and overhead view (b) looks as in the attached image.According to the author of the [paper][2] "The Physics of Putting" the...
  13. H

    Vector space of functions defined by a condition

    ##f : [0,2] \to R##. ##f## is continuous and is defined as follows: $$ f = ax^2 + bx ~~~~\text{ if x belongs to [0,1]}$$ $$ f(x)= Ax^3 + Bx^2 + Cx +D ~~~~\text{if x belongs to [1,2]}$$ ##V = \text{space of all such f}## What would the basis for V? Well, for ##x \in [0,1]## the basis for ##V##...
  14. G

    I What kind of tensor is the gradient of a vector Field?

    (1,1)or(2,0)or(0,2)?And does a dual vector field have gradient?
  15. A

    Is this vector in the image of the matrix?

    Hello! I have this system here $$ \left[ \begin{matrix} -2 & 4 & \\\ 1 & -2 & {} \end{matrix} \right]x +\begin{pmatrix} 2 \\\ y \end{pmatrix}u $$ Now although the problem is for my control theory class,the background is completely math(as is 90% of control theory) Basically what I need to...
  16. L

    A Vector analysis question. Laplacian of scalar and vector field

    If we define Laplacian of scalar field in some curvilinear coordinates ## \Delta U## could we then just say what ##\Delta## is in that orthogonal coordinates and then act with the same operator on the vector field ## \Delta \vec{A}##?
  17. A

    I Rotation of a vector along two axes (of which one is angle-dependent)

    I have been trying to determine an expression for a unit vector in the direction of F for hours now. I think the expression is supposed to look something kind of like this, But I don't understand at all how to arrive at this expression. Any help?
  18. Mayhem

    I Is it valid to express a complex number as a vector?

    ...and is it ever useful? An arbitrary complex number has the form ##z = a + bi## where ##a, b \in \mathbb{R}## and the dot product of two arbitrary vectors ##\vec{v} = \binom{v_1}{v_2}## and equivalently for vector ##\vec{w}## is ##\vec{v} \cdot \vec{w} = v_1 w_1 + v_2 w_3## Then the ##z## may...
  19. T

    Knowing when to decompose weight vector vs. normal vector

    Good afternoon everyone, I have a question on Newton's 2nd Law regarding objects on a generic incline. Take for example, a car on a banked curve: Here in the picture I've provided, you can see that the normal force has been decomposed into the x and y components via sine and cosine of the...
  20. T

    B Notation for a "scalar absolute field"?

    The notation I think best describes it is ## F = \lVert\int^{space}_s|\vec{V}|ds\rVert ## So you have a vector field V in a 3d space. For each point you integrate over all of space (similar to a gravitational or electromagnetic field) *but* vectors in opposite directions do not cancel, they...
  21. LCSphysicist

    The potential electric and vector potential of a moving charge

    I could try to apply the Liénard-WIechert equations immediatally, but i am not sure if i understand it appropriately, so i tried to find by myself, and would like to know if you agree with me. When the information arrives in ##P##, the particle will be at ##r##, such that this condition need to...
  22. G

    I How Can Outward Normal Vector Point Inwards?

    I'm following 《A First Course In General Relativity》.On page 72,it says"If the surface is spacelike,the outward normal vector points outwards.If the surface is timelike,however,the outward normal vector points inwards"I wonder why and how?
  23. T

    I What is the relationship between force and potential in particle interactions?

    Suppose I have some interaction potential, u(r), between two repelling particles. We will name them particles 1 and 2. I want to find the force vectors F_12 and F_21. Would I be correct in saying that the x-component of F_12 would be given by -du/dx, y-component -du/dy etc? And to find the...
  24. chwala

    Solve the problem that involves vector displacement

    My interest is on part ##a## only. Is the markscheme correct? I have ##BA= -b+a= a-b.## It therefore follows that ##|a-b|## is the Length of ##BA##...or are we saying it does not matter even if we have ... ##AB.## Cheers
  25. chwala

    Show that P, Q and D are collinear in the vector problem

    My interest is only on part (b), For part (i), My approach is as follows, ##PB=PO+OB## ##PB=-\dfrac{2}{5}a +b## ##AD=AO+OD## ##AD=-a+\dfrac{5}{2}b## Therefore, ##PB=\dfrac{2}{5}AD## For part (ii), we shall have; ##QD=QB+BD## ##QD=\dfrac{2}{7}AB+\dfrac{3}{2}b##...
  26. S

    Normal vector of an embedding surface

    I will only care about the ##t## and ##x## coordinates so that ##(t, z, x, x_i) \rightarrow (t,x)##. The normal vector is given by, ##n^\mu = g^{\mu\nu} \partial_\nu S ## How do I calculate ##n^\mu## in terms of ##U## given that the surface is written in terms of ##t## and ##x##? Also, after...
  27. G

    I Solving the EM field equations to produce the desired vector field

    So, we have A, the magnetic vector potential, and its divergence is the Lorenz gauge condition. I want to solve for the two vector fields of F and G, and I'm wondering how I should begin##\nabla \cdot \mathbf{F}=-\nabla \cdot\frac{\partial}{\partial t}\mathbf{A} =-\frac{\partial}{\partial...
  28. P

    Parallel RLC Admittance, Current and Power Vector Diagrams

    (An even longer-winded version was written and deleted out of mercy.) Assume an AC voltage at zero degrees applied to an ideal parallel RLC circuit. For a predominantly inductive circuit, the vector diagram for current should show the supply current in the fourth quadrant (i.e. with lagging...
  29. LCSphysicist

    Potential vector of a oscilating dipole:

    I am passing through some difficulties to understand the reasoning to derive the electric potential of an oscilating dipole used by Griffths at his Electrodynamics book: Knowing that ##t_o = t - r/c##, What exactly he has used here to go from the first term after "and hence" to the second term...
  30. Alexanddros81

    I I want to know which software was used to create vector calculus graph

    Hi. I have the Marsden an Tromba vector calculus book 6th edition. I was wondering which software was used to create the books graphs. I attach two graphs as an example. Thanks
  31. breadlover98

    Runge-Lenz vector with perturbation potential

    For the case that there is only a potential ##\sim 1/r##, I have already proven that the time derivative of the Lenz vector is zero. However, I'm not sure how I would "integrate" this perturbation potential/force into the definition of the Lenz vector (as it is directly defined in terms of the...
  32. M

    Mathematica Plot a vector valued function in cylindrical coordinates

    Hi PF! I have a function ##f(s,\theta) = r(s,\theta)\hat r + t(s,\theta)\hat \theta + z(s,\theta)\hat z##. How can I plot such a thing in Mathematica? Surely there's an easier way than decomposing ##\hat r, \hat \theta## into their ##\hat x,\hat y## components and then using ParametricPlot3D?
  33. cianfa72

    I Can a Basis Vector be Lightlike?

    [Moderator's note: Spin off from another thread due to topic change.] I was thinking about the following: can we take as a basis vector a null (i.e. lightlike) vector to write down the metric ? Call ##v## such a vector and add to it 3 linear independent vectors. We get a basis for the tangent...
  34. S

    Vector Diagram of Impulse: Is My Drawing Correct?

    I think all the options are wrong. Since I = Δp = m1v1' - m1v1, I draw it like this: Is my drawing wrong? Thanks
  35. A

    I Electric field vector takes into account the field's radial direction?

    Does the electric field vector takes into account the field's radial direction? Usually when we calculate the electric field, we use ##\vec E = \frac{kq}{r^2}\vec j##, which is a straight line vector of a positive charge q's electric field. This electric field points from a positive charge q to...
  36. J

    Lagrangian with a charged, massive vector boson coupled to electromagnetism

    I need to use hermiticity and electromagnetic gauge invariance to determine the constraints on the constants. Through hermiticity, i found that the coefficients need to be real. However, I am not sure how gauge invariance would come into the picture to give further contraints. I think the...
  37. L

    A Vector analysis and distributions

    In many books it is just written that ##\Delta(\frac{1}{r})=0##. However it is only the case when ##r \neq 0##. In general case ##\Delta(\frac{1}{r})=-4\pi \delta(\vec{r})##. What abot ##\mbox{div}(\frac{\vec{r}}{r^3})##? What is that in case where we include also point ##0##?
  38. M

    Is result of vector inner product retained after matrix multiplication?

    Hi, I was thinking about the following problem, but I couldn't think of any conclusive reasons to support my idea. Question: Let us imagine that we have two vectors ## \vec{a} ## and ## \vec{b} ## and they point in similar directions, such that the inner-product is evaluated to be a +ve...
  39. babaliaris

    Simple Ramp motion problem, but going full vector mode

    Known: 1) The mass of the ball is ##m## (constant ##\frac{dm}{dt} = 0##) 2) ##v(0) = v_{0}## 3) Air drag force magnitude ##| \vec F_{D} | = B \cdot | \vec v(t) |## (##B \in R##) 4) The ramp is frictionless. 5) The magnitude of Earth's acceleration = ##g## I'm not sure if θ is known or not, and...
  40. AimaneSN

    I Finding the orthogonal projection of a vector without an orthogonal basis

    Hi there, I am currently reading a course on euclidian spaces and I came across this result that I am struggling to prove : Let ##F## be a subspace of ##E## (of finite dimension) such that ##F=span(e_1, e_2, ..., e_p)## (not necessarily an orthogonal family of vectors), let ##x \in E## Then...
  41. The Bill

    Applied Resources for general vector differential equations?

    I'd like a good set of notes or a textbook recommendation on how to approach vector differential equations. I'm looking for something that isn't specific to one type of application like E&M, fluid dynamics, etc., but draws heavily from those and other fields for examples. I'd strongly prefer a...
  42. Salmone

    I Derivative of the retarded vector potential

    In a problem of an oscillating electric dipole, under appropriate conditions, one can find, for the potential vector calculated at the point ##\vec{r}##, the expression ##\vec{A}=\hat{k}\frac{\mu_0I_0d}{4\pi}\frac{cos(\omega(t-r/c))}{r}## where: ##\hat{k}## is the direction of the ##z-axis##...
  43. Haorong Wu

    I Coefficients in expansions of a vector potential

    I have seen two expansions of a vector potential, $$\mathbf A=\sum_\sigma \int \frac{d^3k}{(16 \pi^3 |\mathbf k|)^{1/2}} [\epsilon_\sigma(\mathbf k) \alpha_\sigma (\mathbf k) e^{i \mathbf k \cdot \mathbf x}+c.c.],$$ and $$\mathbf A=\sum_\sigma \int \frac{d^3k}{ (2 \pi)^3(2 |\mathbf k|)^{1/2}}...
  44. R

    I Why is momentum considered a vector and kinetic energy a scalar?

    I'm not interested in the mathematical derivation, the mathematical derivation already is based on the assumption that momentum is a vector and kinetic energy is a scalar, thus it proves nothing. Specifically, what happens if we discuss scalarized momentum? What happens if we discuss vectorized...
  45. F

    Find the flux of a vector field

    Question: Equation: Attempt: Can someone verify my answer?
  46. F

    Engineering Find the flux due to a vector crossing an open surface

    Question: Equations: My attempt: Could someone confirm my answer please?
  47. V

    Direction of of the velocity vector for particles in a sound wave

    Using the equations mentioned under this question, I came up with following analysis and directions of velocities on either side of ##x_1##. Also, I'm not sure if there is an easier qualitative way to know the velocity directions rather than do a detailed Calculus based analysis?
  48. MichaelBack12

    Calculus Where Can I Find Online Courses for John Hubbard's Vector Calculus Textbook?

    Anyone know of an online course or set of video lectures on John Hubbard's textbook on Vector Calculus, Linear Algebra, and Differential Forms?
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