Vector Definition and 1000 Threads

  1. G

    Length of spin vector for spin-½ particle

    My answer so far in |S| = √3 /2 *hbar but the question states it must be an angular momentum. Is this an angular momentum or am I missing something? Thanks
  2. W

    Vector problem: Questions about a unit vector

    Not sure how to show that because ##\vec{v} = |v|\hat{v} = 3|e|\hat{e}##, but since ##\vec{e}## is a unit vector we know ##|e| = 1## so our equation now becomes ##\hat{v} = \frac{3\hat{e}}{|v|}##. So, we're left to the task of showing that ##|v| = 3## in order to conclude that ##\hat{v} =...
  3. chwala

    Determine the ratio ##OA:AR## in the vector problem

    My question is on part (c) only. Find the markscheme solution below; Mythoughts on this; (Alternative Method) i used the simultaneous equation ##λ####\left[\dfrac {1}{2}a -\dfrac {1}{4}b\right]##=##\left[ -\dfrac {3}{4}b+ ka\right]## where ##OR=k OA## ##- \dfrac {1}{4}bλ##=## -\dfrac...
  4. C

    B Inverse of a Vector: Find the Correct Form

    What would the correct form of this? $$\stackrel{\leftrightarrow}{A} \cdot \vec{b} = \stackrel{\leftrightarrow}{C} : \vec{d}$$ I'd like to know which one is correct form 1.) $$ \vec{b} = (\stackrel{\leftrightarrow}{A})^{-1} ( \stackrel{\leftrightarrow}{C} : \vec{d} ) $$ 2.) $$ \vec{b} =...
  5. emmanual

    Electric field due to three point charges

    I've calculated the intensity for every point charge which are EA = 6.741 x 10¹³ NC¯¹ EB = 4.494 x 10¹¹ NC¯¹ EC = 6.741 x 10¹³ NC¯¹ and I am pretty sure about this far but I am struggling to calculate the X-axis intensity and Y-axis intensity to find the entire approximate intensity with the...
  6. chwala

    Determine the unit tangent vector

    I need a justification that ##|\dfrac {dr}{dt}|##=##\dfrac {ds}{dt}## cheers guys... all the other steps are easy and clear to me...
  7. chwala

    Determine a unit vector perpendicular to the given planes

    I looked at this question and i wanted to ask if we could also use; ##C## =## c_2 ##(##-\dfrac {3}{2}i## +## j - 3k)## ... cheers This problem can also be solved by using the approach of cross product ##A×B##...
  8. A

    Showing that the gradient of a scalar field is a covariant vector

    In a general coordinate system ##\{x^1,..., x^n\}##, the Covariant Gradient of a scalar field ##f:\mathbb{R}^n \rightarrow \mathbb{R}## is given by (using Einstein's notation) ## \nabla f=\frac{\partial f}{\partial x^{i}} g^{i j} \mathbf{e}_{j} ## I'm trying to prove that this covariant...
  9. runningphysics

    Solving Motion Equations with Integration

    I'm not sure where to start, when I tired using integration of the initial equation to get pos(t)=-.65t^2 i + .13t^2 j + 14ti +13tj but after separating each component, i and j, and setting j equal to zero I got 0 or -100 seconds which doesn't seem like a reasonable answer.
  10. chwala

    Calculate the area of the triangle- Vector Calculus

    This is the question, Now to my question, supposing the vectors were not given, can we let ##V=\vec {RQ}## and ##W=\vec {RP}##? i tried using this and i was not getting the required area. Thanks...
  11. U

    A question on the definition of the curl of a vector

    The curl is defined using Cartersian coordinates as \begin{equation} \nabla\times A = \begin{vmatrix} \hat{x} & \hat{y} & \hat{z} \\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\ A_x & A_y & A_z \end{vmatrix}. \end{equation} However, what are the...
  12. L

    Doubts on Exercise Wording: Energy Density & Poynting Vector

    I have doubts about the wording of the exercise: (1) energy density is ##u=\varepsilon_0 (cB)^2## but since the question asks for mean energy density should I perhaps average over ##cos^2 (\omega t)## (there due to the ##B^2##) and thus use ##<u>=\frac{1}{2}\varepsilon_0 (cB)^2##? (2) it seems...
  13. e2m2a

    I Angular Velocity: Vector or Not?

    I understand that angular velocity is technically not a vector so does that mean the cross product of the radius vector and the angular velocity vector, the tangential vector, is also not a vector?
  14. U

    Finding a vector from the curl of a vector

    Consider the following \begin{equation} \nabla\phi=\nabla\times \vec{A}. \end{equation} Is it possible to find ##\vec{A}## from the above equation and if so, how does one go about doing so? [Moderator's note: moved from a homework forum.]
  15. T

    I Help with electromagnetics: the Poynting Vector and Ampere contradiction

    According to equation (2.33) divergence of the Poynting vector or the outflow of electromagnetic power is equal to the stored magnetic field, stored electric field and ohmic losses. My contradiction is the following: Inside a steady state DC current carrying wire, there will presumably be a...
  16. pellis

    A How to visualise complex vector spaces of dimension 2 and above

    According to e.g. Keith Conrad (https://kconrad.math.uconn.edu/blurbs/ choose Complexification) If W is a vector in the vector space R2, then the complexification of R2, labelled R2(c), is a vector space W⊕W, elements of which are pairs (W,W) that satisfy the multiplication rule for complex...
  17. cianfa72

    I Coord. Time Vector Field: Schwarzschild vs Gullstrand-Painleve

    Hi, I was reading this insight schwarzschild-geometry-part-1 about the transformation employed to rescale the Schwarzschild coordinate time ##t## to reflect the proper time ##T## of radially infalling objects (Gullstrand-Painleve coordinate time ##T##). As far as I understand it, the vector...
  18. yucheng

    Unit Basis Components of a Vector in Tensorial Expressions?

    Divergence formula $$\vec{\nabla} \cdot \vec{A}= \frac{1}{\sqrt{G}} \frac{\partial}{\partial q^{j}} (A^{j} \sqrt{G})$$ If we express it in terms of the components of ##\vec{A}## in unit basis using $$A^{*j} = \sqrt{g^{jj}} A^{j}$$ , we get $$\vec{\nabla} \cdot \vec{A}= \frac{1}{\sqrt{G}}...
  19. M

    How can we define the __mult__ method to return a Complex object?

    Hey! 😊 Construct a class named Vector that expresses the meaning of the vector of numbers. The initialization function, __init__ will take as a argument a tuple corresponding to the vector. This tuple will be stored in the variable named coord. Also, __init__ will calculate the Euclidean...
  20. e2m2a

    I Confusion between vector components, basis vectors, and scalars

    There is an ambiguity for me about vector components and basis vectors. I think this is how to interpret it and clear it all up but I could be wrong. I understand a vector component is not a vector itself but a scalar. Yet, we break a vector into its "components" and then add them vectorially...
  21. cianfa72

    I Gradient as vector vs differential one-form

    It seems to me there is a little of confusion about the definition of gradient. Take for instance a smooth function ##f## defined on a differentiable manifold. Which is actually its gradient at a given point ? Someone says gradient is the vector ##\nabla f## defined at each point, whilst...
  22. NormalForce1

    How Is the Second Leg of the Triangle Calculated in Vector Problem?

    I tried finding the resultant vector which was -6360. The magnitude of -6360 is the distance the traveler must travel to reach the start. I found the angle by using the triangular sum theorem on a right triangle that was split from a scalene triangle. The scalene triangle has side lengths of...
  23. A

    Dependence of the stress vector on surface orientation

    According to Cauchy's stress theorem, the stress vector ##\mathbf{T}^{(\mathbf{n})}## at any point P in a continuum medium associated with a plane with normal unit vector n can be expressed as a function of the stress vectors on the planes perpendicular to the coordinate axes, i.e., in terms of...
  24. S

    I Linear Algebra 1 problem, Vector Geometry: Lines

    Problem: Given the line L: x = (-3, 1) + t(1,-2) find all x on L that lie 2 units from (-3, 1). I know the answer is (3 ± 2 / √5, -1 ± 4/√5) but I don't know where to start. I found that if t=2, x= (-5, 5) and the normal vector is (2, 1) but I am not sure if this information is useful or how...
  25. A

    How to observe if a vector field has curl or not?

    These are the vector fields. I really have no idea how to see if there is a curl or not. I have been looking at the rotation of the vector fields. The fields d and e seem to have some rotation or circular paths, but I read online that curl is not about the rotation of the vector field itself...
  26. Darsh_22

    How do I sketch a flow profile and solve for curl in vector calculus?

    Hello, Can someone explain how to sketch the flow profile in detail. Also, I solved for curl, but I'm getting a zero while the answer is the differentiation of the function f(y). Pls do help me out!
  27. K

    A Change of a vector in a rotating coordinate system

    Goldstein 3 ed, pg 171, under" rate of change of a vector " : The author derives the relationship between the change of a vector in a stationary and rotating coordinate system. In the process he uses this assumption :>It is no loss of generality to take the space and body axes as...
  28. E

    Velocity vector addition problem

    Hello, guys. Interesting riddle here. I have no idea how to solve it. Tried different methods, but point is answer is always wrong, exact answer Downriver, at an angle of 53.13(degree) to the bank. That exercise is from "Pohl’s Introduction to Physics"
  29. K

    A Take your time, and feel free to ask if something is still unclear.

    chapter 4.8 of Goldstein’s classical mechanics 3rd edition that deals with infinitesimal rotations, and the following is the part I got stuck: (p.166~167) : I'm not able to understand what the author is trying to say. How does "If ##d\boldsymbol{\Omega}## is to be a vector in the same sense...
  30. N

    B Vector of forces (question about how a scale works)

    so my question is a little dumb, if an object on a scale has a weight that points downwards and the scale exert normal force on the object upwards cancelling the forces acted on the object then what does the scale read? also the action-reaction pair to the normal force is supposed to be the...
  31. jorgeluisharo

    Vector calculus — Computing this Divergence

    I really don't know how to proceed if I'm not using an specific coordinate system, Is there a way of doing this using only indices, in general form?
  32. guyvsdcsniper

    Help with unit vector for a magnetic field

    So when evaluation the cross product of the velocity of the charge and the unit vectors associated with the point I am getting v x r = j x [ i + j]. Well j x j is 0. j x i = -k, but yet the answer is positive. Why is this?
  33. desperatestudent123

    Calculating magnetic field given dl, current, and radius vector

    I used the above equation, and started with getting the cross product of dl and r, which was equal to 0.00195i+0.00365k. From there, I divided each component by the magnitude of radius cubed (0.827^3). I then multiplied by I and u naught(u_0=4pi*10^-7), and then divided by 4pi. The answer I got...
  34. ergospherical

    A Prove Fermi-Walker Transport of Gyroscope's Spin Vector w/No Applied Moment

    With no applied moments, it is asked to prove that a gyroscope Fermi-Walker transports its spin vector ##S_{\alpha} = - \dfrac{1}{2} \epsilon_{\alpha \beta \gamma \delta} J^{\beta \gamma} u^{\delta}##. In a local inertial frame ##u^{\alpha} = (1, \mathbf{0}) = \delta^{\alpha}_0## and...
  35. Hubble_92

    I Variation of Four-Velocity Vector w/ Respect to Metric Tensor

    Hi everyone! I'm having some difficulty showing that the variation of the four-velocity, Uμ=dxμ/dτ with respect the metric tensor gαβ is δUμ=1/2 UμδgαβUαUβ Does anyone have any suggestion? Cheers, Rafael. PD: Thanks in advances for your answers; this is my first post! I think ill be...
  36. M

    Engineering Solving a Moment Vector Direction Problem: An Example from Statics Textbook

    This isn’t a HW problem per say, but it’s an example shown in my statics textbook that is used to try an explain that you need to add a couple moment to move a force to a point not on the line of action, and I’m just not seeing how the direction of the couple moment is correct. See the image...
  37. mohammed

    Solving Electric Field Vector Problems Using Gauss's Law

    I'm preparing for exam but it seems I can't find problems similar to this on the internet. Here I will apply Gauss's law on the electric field vector to get the charge density. but the problem is that I can't find similar examples on the internet that uses direct vectors on Maxwell's equations...
  38. M

    Engineering Solving Problems Involving Complex Vectors

    Hi Here is my attempt at a solution for problems 1) and 2) that can be found within the summary. Problem 1) a = 3-2i b= -6-4i c= 4+ 6i d= -4+3i Now, to calculate each vector modulus, I applied the following formula: $$\left| Vector modulus \right| = \sqrt {(a^2 + b^2) }$$ where a = real part...
  39. stephenklein

    Conservation of the Laplace-Runge-Lenz vector in a Central Field

    I actually have worked through the solution just fine by taking the derivative of \vec{L}: \frac{d \vec{L}}{dt} = \dot{\vec{v}} \times \vec{M} - \alpha \left(\frac{\vec{v}}{r} - \frac{\left(\vec{v} \cdot \vec{r}\right)\vec{r}}{r^{3}}\right) I permuted the double cross product: \dot{\vec{v}}...
  40. Gustav

    Solving Vector Potential: Calculating Magnetic Field & Difficulties

    My solution for the vector potential ##A=2Cln\frac{x^2+y^2}{z^2} \hat{z}## is: a) I used the following formula to calculate the magnetic field $$ \mathbf{B} = \nabla \times \mathbf{A} = \left( \frac{dA_z}{dy} - 0 \right) \hat{x} + \left( 0 - \frac{dA_z}{dx} \right)\hat{y} + 0 \hat{z} =...
  41. T

    I Vector and Plane Relationship in 3D

    I have a quick question. If a Vector is contained inside a plane, would the normal of the plane be orthogonal to said vector? Thank you!
  42. Blackbear38

    Using Inner Product Properties to Solve Vector Problems

    Summary:: I need to solve a problem for an assignment but just couldn't find the right approach. I fail to eliminate b or c to get only the magnitude of a. Let a, b and c be unit vectors such that a⋅b=1/4, b⋅c=1/7 and a⋅c=1/8. Evaluate (write in the exact form): - ||4a|| - 3a.5b - a.(b-c) -...
  43. O

    Arc length of vector function - the integral seems impossible

    The vector equation is ## v(x)=(e^x cos(2x), e^x sin(2x), e^x) ## I know the arc-length formula is ## S=\int_a^b \|v(x)\| \,dx ## I found the derivative from a previous question dealing with this same function, but the when I plug it into the arc-length function I get an integral that I've...
  44. M

    MATLAB FFT interpretation of time vector (simple)

    I have video data that shows an object moving up and down. I'd like to extract the frequency the object moves. Following the given example here (scroll down to "Examples"), am I correct in assuming Fs would be camera frame rate and L would be the total number of frames? Thanks so much!
  45. A

    I E Vector in E=mc2? Scalar Multiplication & Vectors

    If the energy is a vector, which as i understand for example, the potential energy , U=mgh, where g is the gravitational force, Then U is the product of scalars and vectors, so its a vector In that case being E a vector , can it be equal to mc2 (each are scalars). Like mulitplication of scalars...
  46. Istiak

    Find velocity with vector or without vector

    At the moment he wrote that ##\frac{1}{2}mv_2^2=\frac{1}{2}m(-\dot{y}+\dot{x})^2## But, I know from vector ##v_2=\sqrt{(-\dot{y})^2+(\dot{x})^2}##. At first I (he) found that ##v_2=-\dot{y}+\dot{x}##. But, when thinking of simple velocity in ##x## and ##y## coordinate then I get...
  47. Istiak

    Deriving the Differential Position Vector in Cylindrical Coordinates

    I had an equation. $$T=\frac{1}{2}m[\dot{x}^2+(r\dot{\theta})^2]$$ Then, they wrote that $$\mathrm dr=\hat r \mathrm dr + r \hat \theta \mathrm d \theta + \hat k \mathrm dz$$ I was thinking how they had derived it. The equation is looking like, they had differentiate "something". Is it just an...
  48. guyvsdcsniper

    Where am I going wrong with this vector addition?

    I am following along with an example in my book regarding force from an electric charge. I understand the process but I believe I am getting something wrong when it comes to adding the vectors. Essentially, F13 is equal to -1.35*10^-3 j and when I add that to the j component of F23 which is...
  49. Istiak

    Find the value of ##\theta## when the Vx and Vy components are the same

    The picture may be blurry. I couldn't take more less blurry picture hence, giving it. The question is : Find value of ##\theta## when ##V_x## component and ##V_y## component same. I was using a simple equation of vector. $$C=\sqrt{A^2+B^2+2AB\cos\theta}$$...
Back
Top