Geometric object with magnitude (length) and direction.

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80 views

Curl of a vector field with two different systems of coordinates

Let $$\mathbf{H} = H_x \mathbf{u}_x + H_y \mathbf{u}_y + H_z \mathbf{u}_z$$ be a vector field whose components are defined with respect to the unit vectors $\mathbf{u}_x$, $\mathbf{u}_y$ and ...
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1answer
501 views

Intuitive meaning of Dot Product [duplicate]

I know intuitively that the Cross Product of two vectors $\vec{A}$ and $\vec{B}$ represents another vector $\vec{A \times B}$ perpendicular to it. In study of physics we come across this situation a ...
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2k views

Electromagnetic wave propagation through two lossless dielectrics

In Elements of Electromagnetics (Sadiku, 3rd edition, Section 10.8), the author says to consider two lossless dielectric materials joined at an interface $z=0$. Here two lossless dielectric materials ...
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3k views

Angular displacement and the displacement vector

I've been recently introduced to angular displacement, and I'm a little bit confused about it. I think that displacement which is a vector and which is defined as the shortest distance between any two ...
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128 views

Points in Spacetime

Assume there are two points in spacetime $a=(t,x,y,z)$ and $a'=(t',x',y',z')$. Let's say that the first one is in the origin of spacetime i.e. $a=(0,0,0,0)$. The point $a'$ has two possibilities ...
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286 views

Conservation of Linear Momentum with respect to a given direction

Is linear momentum conserved in any direction? More specifically, if you project all momentum vectors in a system onto another vector, will momentum be conserved? I know that momentum is conserved ...
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268 views

Question on notation in Shankar's Quantum Mechanics - math intro on vector spaces

I'm just beginning Shankar's 2nd edition Quantum Mechanics and having some trouble with notation. He defines his vectors as "$\left|V\right>$" . And with a scalar multiplier as "$a\left|V\right>$" . ...
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395 views

Why no basis vector in Newtonian gravitational vector field?

In my textbook, the gravitational field is given by$$\mathbf{g}\left(\mathbf{r}\right)=-G\frac{M}{\left|\mathbf{r}\right|^{2}}e_{r}$$ which is a vector field. On the same page, it is also given as a ...
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566 views

Vectors, Component Addition, and Significant Figures

I have two vectors $\vec{A}$ and $\vec{B}$ and I need to find the x- and y-components of $\vec{C} = \vec{A} + \vec{B}$. Here's what I have so far: $$|\vec{A}| = 50.0 \mathrm{m}, \theta = ...
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719 views

Acceleration vector - deceleration vs direction

If acceleration of something $= - 10 \text{ m s}^{-2}$ And forwards is define as north. Does that mean the object is getting slower (decelerating) or accelerating in the reverse direction (south) ...
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6k views

The resultant of two forces acting at any angle?

I am studying about forces as vectors. And they give me this equation: $c^2 = a^2 + b^2 - 2ab \cos C$ Can anybody explain me the second part of the equation? I perfectly understand $c^2 = a^2 + b^2$ ...
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1answer
55 views

Newton's third law of motion versus Work

Newton third law of motion says that "To every action, there is always an equal and opposite reaction". The vector study tells us that if two vectors are of same nature and equal magnitude but ...
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38 views

Change of vectors [closed]

We have two vectors $F1$ and $F2$ as shown in figure. The change of vectors is shown as $F2-F1$. Why it is it rather than taking negative of vector $F2$ i.e. $-F2$ and then adding it by head-to-tail ...
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1answer
144 views

Vectors in non-orthogonal systems

In a non-orthogonal coordinate system, what is the physically significant difference between the components of a vector on the skew axes and its projection onto each axis? Why would one want to find ...
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3answers
128 views

Why should multiplication of a ket vector by a complex number change only its “direction”?

Dirac argues on page 17 of his book, The Principles of Quantum Mechanics, that multiplication of a ket by a complex number shouldn't change the state this ket represents. But then concludes: Thus ...
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5answers
104 views

Why is the independence of orthogonal vector-quantities always implicit in books/lectures?

The "theorem" that I can "just" separately deal with orthogonal quantities (like horizontal and vertical force or velocity, etc), I never found explicitly mentioned, but just implicitly in the ...
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1answer
172 views

Understanding vectors in physics: notation

We have the formula for the Lorentz force $$\textbf{F} = q \space(\textbf{E} + \textbf{v} \times \textbf {B})$$ This is a simple formula you learn in high school, but I'm interested to self-study ...
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1answer
200 views

rotation matrix - why am I thinking this wrong?

The rotation given in Question 1 part ii) doesn't match with this wikipedia link http://en.wikipedia.org/wiki/Rotation_matrix. $$ \begin{array}{lcl} x' &=& x \cos\theta - y \sin\theta \\ y' ...
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3answers
108 views

Currents and magnets

I've watched this video on YouTube by Sixty Symbols entitled "Currents and Magnets". In the video, the professor demonstrates the expansion of a wire due to current heating it up and he also ...
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2answers
561 views

Potential of surface charge

I have a question about the $ \hat{n} $ in this formula $\sigma = P \dot{}\hat{n}$. Why do sometime in my book they get $\sigma = P \cos{\theta}$ for a sphere. Isn't $\hat{n} = r$ ? And then in ...
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1answer
380 views

Is there a more clever way to apply the cross product of two vectors to magnetism?

I am just beginning to learn magnetism and my book used two ways to define the force caused by the magnetic field, brushing over the latter. The first: $$F = q v B \sin (\theta).$$ And: ...
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94 views

Derivation of Jefimenko's Equation in Jackson's EMT book

I have been trying to understand the derivation of Jefimenko's equation in Jackson on p.246-247 which can be seen in the photographs attached. First of all I did not fully comprehend the ...
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104 views

Relation between Vector space $V$ and its dual $V^{*}$ [closed]

I asked the same question in Math.SE, but I was suggested to ask it here as well. I am studying relativity, and as you know the theory extensively uses the notion of covariant and contravariant ...
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52 views

Can one representation of a projector operator be re-arranged to get another?

I have a vector space $V$ and a subspace of $V$, $W$. Let $P$ be the projection operator for subspace $W$. Also let the dimension of $W$ be $d$. Also I have two orthonormal basis $(a_1,a_2,...a_d)$ ...
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1k views

How to find total force on an object?

If there are a multitude of forces acting on an object in different directions, how do we find the TOTAL force? I know we add up the $ x $- and $ y $-components of the forces individually, but how do ...
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1answer
105 views

Interpretations of (r,s) tensors [duplicate]

A tensor of type (r,s) on a vector space V is a C-valued function T on V×V×...×V×W×W×...×W (there are r V's and s W's in which W is dual space of V) which is linear in each argument. We take (0, 0) ...
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1answer
122 views

What are some good resources for learning how to apply vectors in physics?

Although I don't have any problems with vectors when using them in Mathematics but I am having a hard time using them in physics. It is really frustrating me. Can you please recommend me some good ...
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304 views

More about the Right Hand Rule?

We started learning about electromagnetism in physics class, and the Right Hand Rule comes in handy as seems easy to use, but I'm curious as to how it actually works. I guess it's more of a math ...
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412 views

Angle needed for object A to intercept with object B

Object B is 15 degrees East of North at a distance of 20km/h. Object B is moving at an average speed of 30km/h in the direction 40 degrees East of North. If object A is capable of moving at 100km/h, ...
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1answer
112 views

Commutation of abstract $O(3)$ generators and vectors [closed]

I've been given the following problem, and I'm quite lost with it. Let $L_1$, $L_2$, and $L_3$ denote the abstract $o(3)$ algebras. You are given that $\vec{A} = (A_1, A_2, A_3)$ and $\vec{B} = ...
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257 views

Spinor formalism in QFT

We can describe fields by two formalisms: vector and spinor. This is the result of possibility of representation of the Lorentz's group irreducible rep as straight cross product of two $SU(2)$ or two ...
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1answer
97 views

How to add magnitude data in an ENU coordiante system

I have water velocity data taken in an ENU (East, North, UP) or XYZ coordinate system. The data is contained in 3 columns like this: ...
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1answer
597 views

Resultant vector problem

$\newcommand{\v}[1]{\vec #1}\newcommand{\i}{\hat i}\newcommand{\j}{\hat j}$ Problem statement (1,2) A shopper at the supermarket follows the path indicated by vectors $\v A, \v B, \v C, \v D$ in ...
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1answer
909 views

Is it possible to prove that the curl of a gradient equals zero in this way?

If $(\nabla\times\nabla\Phi)_i = \epsilon_{ijk}\partial_j\partial_k\Phi$, where Einstein summation is being used to find the $i$th component... Using Clairaut's theorem $\partial_{i}\partial_{j}\Phi ...
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1answer
681 views

Bra space and adjoint vectors

If I'm not wrong, a bra, $ \langle \phi_n | $, can be thought as a linear functional that when applied to a ket vector, $| \phi_m \rangle$, returns a complex number; that is, the inner product it's a ...
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2answers
33 views

Finding the magnitude of Two Vectors [closed]

Vector C has a magnitude 23.4 m and is in the direction of the negative y-axis. Vectors A and B are at angles α = 44.4° and β = 27.7° up from the x-axis respectively. If the vector sum A+B+C = 0, what ...
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3answers
62 views

Why are $2\pi$ factors included in the definition of the reciprocal lattice?

I would like to know where the $2\pi$ factors are coming from in the formula for reciprocal vectors in reciprocal lattices. For example, in a simple cubic lattice the primitive vectors are given by ...
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1answer
29 views

Acceleration in a system equal for every body — why?

A 1 kg cart can slide frictionlessly on the table. The black weights each weigh 1 kg. The pulleys are frictionless. The task is to determine the acceleration of the cart. For the left-most ...
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71 views

Do components of force have direction when doing work?

When we get angle > 0, the x-component of force is along the direction of displacement and so their product is called Work. So the x-component of force is said to have direction of the respective ...
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1answer
80 views

What is the work done said when angle between force and displacement>90 and <180?

If the angle between $Force$ and $Displacement$ is obtuse then by using the formula of $Work$ we get negative quantity so is it said then that the system is losing energy or it is merely for the case ...
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1answer
30 views

Computing the Initial Velocity of an orbiting body

I'm working on a simulation program that replicates the movement of planets around a large celestial body (the sun). This is a three dimensional simulation that uses vectors. At present, I'm ...
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1answer
34 views

How to expand this equation considering acceleration due to gravity into 3D vector space?

How can we expand this following equation into 3D vector space? I learned this equation from this answer: Don't heavier objects actually fall faster because they exert their own gravity? The ...
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1answer
50 views

What does it mean by $t=-1$?

if the position vector of a particle is $\hat{r}=\left(4+3t\right)\hat{\imath}+\left(t^3\right)\hat{\jmath}+\left(-5t\right)\hat{k}$, i want to find at what time this particle passes through the point ...
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1answer
140 views

How to show that the force and velocity are perpendicular and that both have constant magnitude? [closed]

The force acting on a moving charged particle in a magnetic field $\hat{B}$ is $\hat{F}=q\left(\hat{v}\times \hat{B}\right)$ where $q$ is the electric charge of the particle, and $\hat{v}$ is its ...
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237 views

Why is force a localized vector and not a free vector?

A vector which is drawn parallel to a given vector through a specified point unlike free vector in space is called a localised vector. The effect of a force acting on a body depends not only on the ...
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1answer
437 views

How can I calculate the speed of an object knowing its horizontal and vertical velocity components?

Let's say a ball is thrown and it experiences typical projectile motion (moves in a parabolic arc etc.) and the only information we know are the equations for the horizontal and vertical components of ...
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1answer
79 views

Vectors-Can anyone explain me the concept of sense in vectors?

Is it same as the direction?Then , why another term "sense"is used ,instead of direction? Can anyone illustrate it?
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108 views

Integral ambiguity

I'm a bit confused with some notation I encounter in physics calculus. Consider this: Taken from here. Integration operates on functions, correct? What does it mean to integrate $\frac{d{\bf ...
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165 views

Free vs bound vectors and torque

When considering basic Newtonian mechanics, we can treat vector as free and move their point of application at will. This is consistent with the affine nature of Euclidean space. However, when ...
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182 views

How do I find the perpendicular velocity of a particle to a varying magnetic field?

I am trying to find the component of velocity perpendicular to a magnetic field. This was easy when the magnetic field was static and pointing in only one direction (the $z$ axis), but now I need to ...