Geometric object with magnitude (length) and direction.

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0answers
22 views

equilibrium of particles in space

So I'm asked to find d and also determine the tensions in cable BD and AD. Getting the vector components and then multiplying them with the corresponding tension should equate the sum of the force ...
0
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0answers
14 views

How do I subtract and add vectors? [on hold]

For the vectors shown in Fig. 3-32 (A = 64.0 and θ = 56.0°), determine the following. Fig. 3-32 = http://imgur.com/pdGd3Pt (a) C - A - B Find the magnitude and direction (b) 2A - 3B + 2C Find ...
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0answers
51 views

Vector calculus problem [on hold]

I have to solve this: $$[(\nabla \times \nabla)\cdot \nabla](x^2 + y^2 + z^2)$$ But I am really drowning in the sand.. Can anybody help me please?
1
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0answers
650 views

Squaring a Vector? [migrated]

So this one is basic. And should be pretty quick. Lets say that I have a vector $\vec{r}$: $\vec{r} = \vec{x} + \vec{y} + \vec{z}$ Is this true: $\vec{r}^{2} = \vec{x}^{2} + \vec{y}^{2} + ...
-1
votes
0answers
24 views

Proof of transformation between contravariant and covariant components of vector [on hold]

What is the proof of the relation ${g^{ir}g_{rj}=\delta^i_{j}}$ where ${g}$ is the metric tensor and ${\delta}$ is the Kronecker delta. EDIT:The operations is known as equivalent to raising and ...
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1answer
39 views

Differentiation of a vector with respect to a vector

Does differentiation of a vector with respect to a vector make any sense? Even if it makes sense, how does it make any physical meaning? I mean what is the physical interpretation?
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votes
1answer
18 views

Statics Vector Question [closed]

I need help with this problem image of problem: http://postimg.org/image/87o0tyfyp/ I could answer the question if I had a second angle but I don't even know where to begin to solve the question. ...
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3answers
57 views

Curl of a vector [on hold]

What is the physical interpretation of curl of a vector? Please give some common examples in Physics. Just as divergence implies flux through a surface.
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2answers
72 views

Very basic question about vector

The vectors $a = (2,-1,-2)$ and $b = (0,-3,4)$ are given. Determine $a$:s parallel and normal vector to $b$. Obviously the parallel vector should be the dot product $a \cdot b$ times the unit vector ...
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1answer
51 views

Basic Notation Help Needed : Classical Mechanics, Unit Vectors

Can someone help me with some basic notation? Here's a situation where I'm surely missing some trivial piece of the puzzle: Example 1: given $W = \frac{1}{2}cpAv^2$ (air resistance), adding a unit ...
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0answers
67 views

Proof for parallelogram law of vector addition [migrated]

The Statement of Parallelogram law of vector addition is,If two vectors are considered to be the adjacent sides of a Parallelogram, then the resultant of two vectors is given by the vector which is a ...
0
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0answers
25 views

Using the dipole moment to calculate the electric potential

I have the following defintion of dipole moment given: $$ \vec{p} := \int\vec{r}'\rho(\vec{r}')dV $$ Where $\rho$ is a charge density function and $\vec{r}'$ traces out the body of charge. I am ...
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2answers
76 views

Transformation of four-velocity in special relativity

I am revising special relativity introducing more matrix form in the equation. Currently I am reading book in which transformation matrix is defined as $${\Lambda= \begin{bmatrix} \gamma & ...
0
votes
1answer
52 views

When will the velocity of a particle be perpendicular to it's initial velocity?

I am learning kinematics with vector analysis. I was given the position equation:$\mathbf{r} = 10t\hat{\mathtt{i}} + (20t-5t^2)\hat{\mathtt{j}}$. It asks me the time when the velocity of the particle ...
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1answer
45 views

Derivation of vector cross product [duplicate]

Everyone of us know about the vector cross product. But I wonder, how the formula of $AB\sin\theta$ has been derived? Can anyone help?
0
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1answer
11 views

Clarification needed:Projection Or Whole Length to be considered during integration

Sometimes in magnetism,electrostatics,friction problems when a force is acting over a curved we usually take the net projection of the curved path as the distance(to avoid integration).But it certain ...
2
votes
2answers
51 views

Geometric definition of the Lorentz inner product

In Euclidean space one can define the dot product as projecting one vector to the other and multiply the length of the projected vector with the length of the other vector. This definition doesn't ...
0
votes
2answers
51 views

What should the brake force in this problem be? [closed]

Alright so I think I know how to do this but I require help in calculating what acceleration would be in terms of some sort of friction coefficient. So model a particle going down a hill. The slope ...
0
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2answers
33 views

Distance traveled from displacement

I am currently reading a book called Physics for Scientists and Engineers by Serway. While reading the chapter about 2-dimensional kinematics, I asked myself a ...
13
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5answers
666 views

What does it mean for a physical quantity if its mixed second partial derivatives are not equal?

This goes for every problem (either in electromagnetism or fluid dynamics) that has to do with vector fields. Say we have a fluid flowing in a closed circular pipe (or an electromagnetic field, the ...
2
votes
2answers
86 views

What coordinate systems allows the magnitude of the basis vectors to change with position?

I'm familiar with coordinate systems where the direction of the basis vectors changes with position, but I haven't come across any where the relative magnitude of the basis vectors themselves are ...
0
votes
3answers
89 views

Difference between $|d{\bf r}|$ and $d|{\bf r}|$

What is the difference between $|d{\bf r}|$ and $d|{\bf r}|$ and why are both of them not always equal to each other? My question might seem stupid to some and will probably get downvoted but I have ...
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2answers
70 views

Is torque still a vector in 2 Dimensions?

In 3D, torque is defined as $\vec{r} \times \vec{F}$ which is a vector, therefore having both a direction perpendicular to the plane of $\vec{F}$ and $\vec{r}$ and a magnitude of ...
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2answers
39 views

Is the displacement vector tangent to the circular path?

My book says that when a mass travels in a curved path, like a circle for example, the instantaneous velocity and displacement vectors are both tangent to the path. I agree that velocity vector ...
1
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3answers
78 views

Is there a general rule for determining the direction of tension force?

Tension, for me, is a tricky thing. After finishing a related chapter of my book and watching a video, I still can't get a hang of it. Here is a situation: My knowledge is that tension, just like ...
0
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1answer
31 views

How do I get the angle for the $x$ and $y$ component of the electric field for four equidistant particles?

Four particles form a square of edge length $a= 5.00\ cm$ and have charges $q_1= +10\ nC$, $q_2=-20\ nC$, $q_3=20\ nC$, and $q_4=-10\ nC$. In unit vector notation, what is the net electric field the ...
1
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1answer
63 views

Coulomb's law with an $r^3$, not $r^2$, in the denominator [duplicate]

I am reading an older physics book that my professor gave me. It is going over Coulomb's law and Gauss' theorem. However, the book gives both equations with an $r^3$, not $r^2$, in the denominator. ...
0
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1answer
26 views

Co-ordinate rotations

I need help transforming a magnetic field vector from one co-ordinate system to another. I have the components of the Earth's magnetic field in a co-ordinate system with z facing radially into the ...
5
votes
2answers
311 views

How does one write Newtons 2nd Law using the language of forms?

Newton's second law says that $F=ma$. Supposing that the force is conservative and can thus be expressed in terms of a potential $V$ we have that $F=-dV$. We have that $V$, being a function, can ...
1
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1answer
31 views

A way to determine if a body accelerates or loses speed at a certain time

With given vectors for acceleration and velocity, is there a way to determine if a body accelerates or decelerates at a certain time-interval? Can this be determined, for instance, by simply observing ...
0
votes
1answer
51 views

Explain how $\Delta v_{\perp}=v\Delta\theta$

In The Feynman lectures, under the chapter entitled Vectors, Feynman writes: My two intimately related questions are: 1) What does he mean by the magnitude of velocity? is he talking about the ...
0
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0answers
26 views

Does dimensionality determine the net effects of randomly oriented forces on an object?

My question relates to the orthogonality of random vectors in high dimensional space, and the relationship of random vectors as a function of dimensionality. My question can be formulated as a ...
0
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1answer
61 views

Why would the norm of these vectors be 1?

Let a Cartesian coordinate system $uOx$ coincides with a vertical plane so that $Ou$ is the horizontal axis and $Ox$ is the axis oriented vertically upwards (see Fig. 1). We are looking for the ...
1
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1answer
82 views

Vector product in a 4-dimensional Minkowski spacetime

I'm studying relativity and I lost track of interpretation along the mathematical formalism. What does vector product mean as an event? I mean, how must one interpret the result of the vector product ...
0
votes
3answers
194 views

resultant of 3 vectors along sides of equilateral triangle [closed]

It is a homework problem, but I really don't quite understand the question. It reads- "3 forces of magnitudes 10N, 20N, and 30N acting on a point are parallel to the sides of an equilateral triangle, ...
6
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3answers
1k views

Does spacetime position not form a four-vector?

When one starts learning about physics, vectors are presented as mathematical quantities in space which have a direction and a magnitude. This geometric point of view has encoded in it the idea that ...
2
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0answers
44 views

Moment line of action

I am having trouble understanding a moment's line of action. Lets say we have door hinge of $L$ length and push down on it with $X$ force. The moment at the begin $(O)$ of the hinge would then be ...
1
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2answers
90 views

What does it mean by saying the generators of translations transform as vectors under the Lorentz Group?

The commutator of generators of Lorentz transformation and translation is as follow: $$[M^{\mu\nu},P^\sigma]=i(P^\mu\eta^{\nu\sigma}-P^\nu\eta^{\mu\sigma} ).$$ Then from this we usually say that the ...
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1answer
69 views

Are perpendicular components special in vectors?

We can split a vector (velocity/displacement vector) along any two directions as long as the resultant of the oblique components of the vector is same as my original vector. Similarly if we have to ...
1
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1answer
51 views

Clarifying some notation, the square of a vector derivative

I'm reading a text which asserts that, if $\vec{F}(\vec{x})=-\nabla V(\vec{x})$ then we define $$E = \frac{m}{2} \left( \frac{d\vec{x}}{dt}\right)^2-V(\vec{x}) \, .$$ However, I don't understand how ...
0
votes
4answers
150 views

Is magnitude of velocity same as speed?

Is magnitude of instantaneous velocity same as instantaneous speed? More specifically, is $$\left|\frac{d\vec{r}}{dt}\right| = \frac{d|\vec{r}|}{dt}\; .$$ Also Is it wrong to say that ...
0
votes
3answers
249 views

Can we have physical quantities which have magnitude and direction but are not vectors?

I am not able to understand how to approach the question. Vectors are defined as quantities having magnitude and direction, then how is it possible? Please explain.
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2answers
34 views

Problem with velocity vector [closed]

Question: The radius vector of a point depends on time $t$, as $\vec{r} = \vec{c}t+\dfrac{\vec{b}t^2}{2}$ where $c$ and $b$ are constant vectors. Find the magnitude of velocity. My attempt : ...
0
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3answers
173 views

How do we calculate instantaneous velocity in 2D?

Suppose a body is moving with a constant speed of $10~\mathrm{ms^{-1}}$ in negative $x$ direction in $x$-$y$ plane. Let $\vec r$ be the position vector. Then what will be the instantaneous velocity ...
1
vote
2answers
79 views

Clarification on meaning of scalar in math and scalar in physics

When a mathematician says something is a scalar, say on the plane, they mean that it associates to points on the plane real numbers. When a physicist says something is a scalar, they mean that if we ...
0
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2answers
51 views

Dirac notation and column representation

$\renewcommand{ket}[1]{|#1\rangle}$ I am facing difficulty in understanding how the right hand side is coming in equation A below In $H$ of dimention 4, the vector $$ \sqrt{\frac{2}{3}} ...
4
votes
4answers
259 views

Why perpendicular vectors do not share components?

I just can picture it in my mind or on paper. Can someone explain it with examples? This is the key idea behind the uniform circular motion: if the force has a component in direction of the object's ...
-1
votes
1answer
56 views

Angle between vector and $x$-axis [closed]

I have to find to component of vector DE having magnitude 1 m .now the vector is in 4th quad making angle 90 degree with postive x axis The solution that my teacher showed is ax=1cos(270) .and ay = ...
0
votes
2answers
82 views

Gauss' Law and area vector

Recently I've been doing some physics exercises on electric and magnetic fields and read up somewhere that the vector area of a closed surface is equal to zero. That made me wonder why, when using ...
0
votes
1answer
65 views

Is it better to walk or run when there is rain? [duplicate]

When I was coming from school to my house, there was heavy rain. Then one of my friends said "Don't simply walk, run fast". Then the question came to my mind: how should I go so as to avoid wetting: ...