Vector Definition and 1000 Threads

  1. G

    I No interference if orthogonally polarized

    Hi. A beam of previously unpolarized or diagonally polarized doesn't create an interference pattern behind a double slit if there is a vertically and horizontally oriented polarizer behind either slit. The classical explanation is that the electric field is a vector perpendicular to the...
  2. Krushnaraj Pandya

    Vector of shortest distance between two skew lines

    Homework Statement how to write the vector equation of the line of shortest distance between two skew lines in the shortest and most efficient way? (The exact lines given in a particular problem in my book can be referenced- L1=(3i+8j+3k)+λ(3i-j+k) and L2=(-3i-7j+6k)+μ(-3i+2j+4k) ) 2. Relevant...
  3. Krushnaraj Pandya

    Relation between vector length and direction ratios

    Homework Statement A vector r has length 21 and direction ratio's 2,-3,6. The direction cosines of r, given that r makes an obtuse angle with x-axis is given by? Homework Equations l/a = m/b =n/c ...(1) (l,m,n are direction cosines, a,b,c are direction ratios l^2 + m^2 + n^2=1...(2) The...
  4. Specter

    Find the scalar, vector, and parametric equations of a plane

    Homework Statement Find the scalar, vector, and parametric equations of a plane that has a normal vector n=(3,-4,6) and passes through point P(9,2,-5) Homework EquationsThe Attempt at a Solution Finding the scalar equation: Ax+By+Cz+D=0 3x-4y+6z+D=0 3(9)-4(2)+6(-5)+D=0 -11+D=0 D=11...
  5. S

    Optimizing Dolphin Tracking: Calculating the Angle for Dart Gun Accuracy

    Homework Statement A scientist investigating the movements of dolphins in the Mediterranean uses a dart gun to shoot small, harmless tracking devices onto the fins of dolphins. When standing on deck, her hand is 1m above the water, and looking along the dart gun she is holding at an angle of...
  6. Specter

    Writing vector and parametric equations for a line that....

    Homework Statement [/B] Write vector and parametric equations for the line that goes through the points P(–3, 5, 2) and Q(2, 7, 1). Homework EquationsThe Attempt at a Solution First I find the direction vector for PQ. PQ=Q-P = (2,7,1)-(-3,5,2) =[2-(-3),7-5,1-2] =5,2,-1 PQ= (5,2,-1) Now I...
  7. L

    Torque and Angular Momentum - Origin Misconception

    Homework Statement (Problems/diagrams referenced are attached as images.) Homework Equations Net torque about an origin = time derivative of the angular momentum vector about the same origin. The Attempt at a Solution I've solved these problems before, but I'm now looking back at them and...
  8. Hawkingo

    B Can a Scalar Operate with a Vector Algebraically?

    Let ##\vec { A }## = ##a \dot { i } + b \hat { j } + c \hat { k }## My question is "is ##\frac { 1 } { \vec { A } }## is a vector or not and if yes then what is it's components?"
  9. Abdu Ewais

    I Problem with gravitation field perpendicular vector.

    since it is known that ##\vec{A_\perp} = -{mG \over R^2}## why did the professor write it as ##\vec{A_\perp} = {- R G \rho \over 3}## for perfect sphere with perfect mass distribution ? Shouldn't it be ##\vec{A_\perp} = -{4 \over 3} \pi R G \rho##? I need help thanks.
  10. bushabean

    Trouble dealing with vector coordinates in question

    Homework Statement A rocket is to rendezvous with a satellite and needs to make a course adjustment. the rocket has a velocity = (10 + 0 + 0) ms−1 relative to the satellite and mission control has sent a command to the rocket side thruster to exert a thrust = (0 − 100 + 0) N for 100 seconds...
  11. L

    Quick Question: Rate of Change of a Rotating Vector

    Is the equation presented (that the time-derivative of a given vector in such a scenario is equal to its angular frequency vector cross the vector itself) true in the case of a vector whose origin is not on the axis of rotation? The way I'm visualizing this, if we take such a displaced origin...
  12. K

    I Displacement vector in general relativity

    Is there a sensible way of defining a displacement vector in a general manifold? That is, the displacement vector being the difference between position vector at two different points... the problem is that these two different points have, in general, different tangent vector spaces. Never the...
  13. F

    I Apparent Poynting vector contradiction

    Hello all, Im trying to do a simulation of a poynting vector of an electromagnetic wave and I assume the following: At t=0 the E-field vector is (0,0,e^(-ikx)) and the H-field vector (0,e^(-ikx),0), hence orthogonal to it in vaccum, which is assumed, also the amplitudes are simplified both to...
  14. CptXray

    Finding integral curves of a vector field

    Homework Statement For a vector field $$\begin{equation} X:=y\frac{\partial{}}{\partial{x}} + x\frac{\partial{}}{\partial{y}} \end{equation}$$ Find it's integral curves and the curve that intersects point $$p = \left(1, 0 \right).$$ Show that $$X(x,y)$$ is tangent to the family of curves: $$x^2...
  15. E

    A Lie derivative of vector field defined through integral curv

    Consider ##X## and ##Y## two vector fields on ##M ##. Fix ##x## a point in ##M## , and consider the integral curve of ##X## passing through ##x## . This integral curve is given by the local flow of ##X## , denoted ##\phi _ { t } ( p ) .## Now consider $$t \mapsto a _ { t } \left( \phi _ { t } (...
  16. Hawkingo

    B How to specify the direction of an area vector?

    We all know that the area of a triangle having consecutive sides as ##\vec { a }## and ##\vec { b }## has the area ##\frac { 1 } { 2 } | \vec { a } \times \vec { b } |## but what is the direction of that area vector? I mean if we consider ##\vec { a } \times \vec { b }## that will be one...
  17. George Keeling

    Covariant coordinates don't co-vary

    Homework Statement I am studying co- and contra- variant vectors and I found the video at youtube.com/watch?v=8vBfTyBPu-4 very useful. It discusses the slanted coordinate system above where the X, Y axes are at an angle of α. One can get the components of v either by dropping perpendiculars...
  18. A

    A How to find the displacement vector in Spherical coordinate

    Is there a way of subtracting two vectors in spherical coordinate system without first having to convert them to Cartesian or other forms? Since I have already searched and found the difference between Two Vectors in Spherical Coordinates as...
  19. M

    MHB The axioms of a vector space are satisfied

    Hey! :o We consider the $\mathbb{F}_2$-vector space $(2^M, +, \cap)$, where $M$ is non-empty set and $+ : 2^M\times 2^M \rightarrow 2^M: (X,Y)\mapsto (X\cup Y)\setminus (X\cap Y)$. I want to show that $(2^M, +, \cap )$ for $\mathbb{K}=\{\emptyset , M\}$ satisfies the axioms of a vector space...
  20. M

    MHB Vector space - Prove or disprove

    Hey! :o Let $1\leq n\in \mathbb{N}$ and let $U_1, U_2$ be subspaces of the $\mathbb{R}$-vector space $\mathbb{R}^n$. I want to prove or disprove the following: The set $\{f\in \mathbb{R}^{\mathbb{R}} \mid \exists x\in \mathbb{R} : f(x)=0_{\mathbb{R}}\}$ is a subspace of...
  21. Glenn Rowe

    A Polarization vector sums in QED

    I'm working through Lahiri & Pal's book A First Book of Quantum Field Theory, Second Edition and I'm stuck on their explanation of the polarization vector in quantum electrodynamics in Chapters 8 and 9. In section 8.8, they derive a formula for the sum over the transverse polarization modes of...
  22. T

    Why is force vector F but acceleration vector a not A?

    Is there some rule or standard that determines whether we define a vector with upper or lower case? I have not been told of any particular rule but it seems with velocity and acceleration they are lower case but force has always been upper case from what I've been reading so far. Is there a...
  23. I

    I Calculating Divergence of a Vector Field in Three Dimensions

    If I have a vector field say ## v = e^{z}(y\hat{i}+x\hat{j}) ##, and I want to calculate the divergence. Do I only take partial derivatives with respect to x and y (like so, ## \frac{\partial A_x}{\partial x} + \frac{\partial A_y}{\partial y} ##) or should I take partial derivatives with respect...
  24. T

    Vector Calculus: Change of Variables problem

    Homework Statement Let D be the triangle with vertices (0,0), (1,0) and (0,1). Evaluate: ∫∫exp((y-x)/(y+x))dxdy for D by making the substitutions u=y-x and v=y+x Homework EquationsThe Attempt at a Solution So first I found an equation for y and x respectively: y=(u+v)/2 and x=(v-u)/2 Then...
  25. jonathanm111

    Vector Calculus, setting up surface area integral.

    The question goes like: find the SA of the portion S of the cone z^2 =x^2 +y^2 where z>=0 contained within the cylinder y^2+z^2<=49 this is my attempt using the formula for SA, I could switch to parametric eqns, but even then I'd have hard time setting up limits of integration.
  26. N

    Does a Circular Capacitor with a Dielectric Radiate an Electromagnetic Field?

    Hi guys, Consider a circular capacitor with a disk of radius a and plate separation d, as shown in the figure below. Assuming the capacitor is filled with a dielectric constant epsilon and the capacitor is fed by a time harmonic current I0 (a) Find the magnetic field distribution inside the...
  27. twoski

    Vector projection to other vector

    Let's say i have 2 arbitrary vectors in a 3d space. I want to project Vector A to Vector B using a specified normal. edit: better image A is green, B is red, C is red arrow. Blue is result. In this case, i want to project green vector to red vector in the red direction. This would give me...
  28. Celso

    Nullifying Lorentz Force on Proton Moving in Parallel Direction

    Homework Statement A proton moves with a speed ##v = 3 \cdot 10^5 \frac{m}{s}## in the parallel direction to ##i+k##. A magnetic field of ##1T##, in the ##i+j+k## acts over it. Which electric field must we apply in this region so that the Lorentz force over the proton is null? Homework...
  29. Robin04

    Solving 3D Vector Equation for ##\vec{y}##

    Homework Statement Solve the following vector equation for ##\vec{y}##. ##\vec{a}##, and ##\vec{b}## are linearly independent vectors of the three dimensional space. ##\vec{a} \times (8\vec{y}+\vec{b}) = \vec{b}\times(-5\vec{y}+\vec{a})## Homework EquationsThe Attempt at a Solution First I...
  30. O

    Change of basis computation gone wrong....

    Homework Statement Consider the real-vector space of polynomials (i.e. real coefficients) ##f(x)## of at most degree ##3##, let's call that space ##X##. And consider the real-vector space of polynomials (i.e. real coefficients) of at most degree ##2##, call that ##Y##. And consider the linear...
  31. K

    I Gradient vector without a metric

    Is it possible to introduce the concept of a gradient vector on a manifold without a metric?
  32. K

    Vector representation of Lorentz group

    Homework Statement In this problem, we'll construct the ##(\frac{1}{2},\frac{1}{2})## representation which acts on "bi-spinors" ##V_{\alpha\dot{\alpha}}## with ##\alpha=1,2## and ##\dot{\alpha}=1,2##. It is convential, and convenient, to define these bi-spinors so that the first index...
  33. H

    I Represenation of a state vector in a different basis

    Is it possible to expand a state vector in a basis where the basis vectors are not eigenvectors for some observable A? Or must it always be the case that when we expand our state vector in some basis, it will always be with respect to some observable A?
  34. Zeynel

    B The definition of “vector” in math and physics

    I'm learning APL and this is how a vector is defined https://tryapl.org: All data resides in arrays. An array is a rectangular collection of numbers, characters and arrays, arranged along zero or more axes. We can use more specific terms for some arrays, like a single number is a scalar, a list...
  35. DuckAmuck

    I Can any matrix be expressed as the product of two vectors?

    For example, does this always hold true? M_ab = v_a × w_b If not, where does it break down?
  36. E

    MHB Oblique projection of a vector on a plane

    Suppose a plane contains the origin and has normal $n$. Is it true that the projection of a vector $u$ on the plane along vector $v$ is $(v\times u)\times n$, where $\times$ denotes the cross product? I can see that the direction is right, but I am not sure about the length. Links to textbooks...
  37. M

    How do I find a plane that contains two given lines?

    Homework Statement a. Find a point at where these lines intersect b. Find the equation of a plane that contains the two lines. Homework Equations r[/B] = <1,3,0> + t<3,-3,2> r = <4,0,2> + s<-3,3,0> The Attempt at a Solution I correctly found the point of intersection to be...
  38. R

    B Confusion about the radius unit vector in spherical coordinates

    If the radius unit vector is giving us some direction in spherical coordinates, why do we need the angle vectors or vice versa?
  39. N

    I Why vector lengths may not be preserved?

    Given some metric, what is an example where the length of a vector is not preserved?
  40. M

    Convert a spherical vector into cylindrical coordinates

    Homework Statement Convert the vector given in spherical coordinates to cylindrical coordinates: \vec{F}(r,\theta,\varphi) = \frac{F_{0}}{arsin\theta}\bigg{[}(a^2 + arsin\theta cos\varphi)(sin\theta \hat{r} + cos\theta \hat{\theta}) - (a^2 + arsin\theta sin\varphi - r^2 sin^2\theta)...
  41. archaic

    B Dot product scalar distributivity

    I'm having a little trouble with this : We have ##(\alpha\vec{a})\cdot b = \alpha(\vec{a}\cdot\vec{b})## but shouldn't it be ##|\alpha|(\vec{a}\cdot\vec{b})## instead since ##||\alpha \vec{a}||=|\alpha|.||\vec{a}||## ? ##(\alpha\vec{a})\cdot b = ||\alpha\vec{a}||.||\vec{b}||.\cos\theta =...
  42. aboutammam

    I About the properties of the Divergence of a vector field

    Hello I have a question if it possible, Let X a tangantial vector field of a riemannian manifolds M, and f a smooth function define on M. Is it true that X(exp-f)=-exp(-f).X(f) And div( exp(-f).X)=exp(-f)〈gradf, X〉+exp(-f)div(X)? Thank you
  43. C

    Create the free-body diagram for the scenario below.

    Homework Statement A Mercedes-Benz 300SL (m = 1700 kg) is parked on a road that rises 15 degrees above the horizontal. What are the magnitudes of (a) the normal force and (b) the static frictional force that the ground exerts on the tires? Important: Assume that the road is higher up to the...
  44. D

    I Integration of the gradient of a vector

    Hi. Is it true to say that the integral over all volume of ∇ψ where ψ is a scalar function of position and time is just ψ ? Thanks
  45. Specter

    Proving the associative property of vector addition

    Homework Statement Give an example of the associative property of vector addition using vectors in Cartesion form. Homework Equations (u+v)+w=u+(v+w) The Attempt at a Solution I can't figure out how to get the arrow on top of my work so I wrote it without it. I'm somewhat confused on why I...
  46. jonathanm111

    Vector Calculus (non conservative vector fields

    the question: My attempt: The partial derivatives did not match so i simply tried to find f(x,y) I got the set of equations on the right but that's about it.
  47. CivilSigma

    What is the equation for determining the magnitude of a vector in 2D space?

    Homework Statement For any vector in 2D space, it can be broken down into its horizontal and vertical components. Homework Equations In one of my engineering classes, we are using the following equation to determine the magnitude of a vector: $$u=v_1 \cdot cos\theta +u_2 \cdot sin\theta$$...
  48. prashantakerkar

    B Is Equilibrium a Scalar or Vector Quantity?

    1 Is Equilibrium a Scalar or Vector quantity? 2 What is the unit of Equilibrium? Thanks & Regards, Prashant S Akerkar
  49. alexi_b

    Finding the angle in which the resultant force points

    Homework Statement Forces of 11.8N north, 19.2N east, and 15.9N south are simultaneously applied to a 3.93kg mass as it rests on an air table. What is the magnitude of its acceleration? What is the direction of the acceleration in degrees? (Take east to be 0 degrees and counterclockwise to be...
  50. karush

    MHB 307.8.1 Suppose Y_1 and Y_2 form a basis for a 2-dimensional vector space V

    nmh{796} $\textsf{Suppose $Y_1$ and $Y_2$ form a basis for a 2-dimensional vector space $V$ .}\\$ $\textsf{Show that the vectors $Y_1+Y_2$ and $Y_1−Y_2$ are also a basis for $V$.}$ $$Y_1=\begin{bmatrix}a\\b\end{bmatrix} \textit{ and }Y_2=\begin{bmatrix}c\\d\end{bmatrix}$$ $\textit{ then }$...
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