Geometric object with magnitude (length) and direction.

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1answer
26 views

$F\cos\theta$ is not proportional to $d\cos\theta$?

If Iā€™m working in two dimensions and I wanted to calculate the net electrostatic force on charge C, where charges A and B are stationary, of the same charge, and placed on the y-axis equidistant ...
0
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0answers
11 views

Tensor product distributive property?

Is it true that for vectors a,b,c,d we have $$|a> \otimes |b> <c| \otimes <d|= |a><c| \otimes |b><d|?$$ So does this kind of distributive law hold for tensor products?
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0answers
23 views

Calculus Based Physics Problem with Particle Motion [on hold]

Suppose the position vector for a particle is given as a function of time by $$\hat{r}(t) = x(t)\hat{ i} + y(t)\hat{j}$$ while $$x(t)=at+b \text{ and }y(t)=c(t^2)+d,$$ where $a=1.00\, m/s$, $b=1.00\, ...
-4
votes
0answers
29 views

How to determine the resultant vector of 2 parallel vectors geometrically on a Euclidean plane? [on hold]

Suppose, 2 vectors are given on plane. Then how would I draw the resultant vector geometrically? I didn't find anything useful on Google. So I am asking for help.
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0answers
33 views

Reducing a vector calculus relation [on hold]

Someone can help me? I want to reduce this. $$ (\nabla \times \mathbf{B}) \times \mathbf{B} + (\nabla \times \mathbf{B}) $$ Thanks
-1
votes
1answer
42 views

Find the indicated quantities from the given data [on hold]

This is a vector application. A rope is hung at both ends from a horizontal beam, and a weight m is suspended from it as shown in the figure. The left part of the rope exerts a force G at P, while ...
0
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2answers
21 views

Definition of Position Vectors

I have a few (possibly very stupid) questions relating to position vectors; more specifically my confusion about them. Following Halliday and Resnick's text, we define vectors by their magnitude and ...
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0answers
23 views

vector addition and subtraction

. Vector A has a magnitude of 20 m and makes an angle of 30āˆ˜ above the positive x axis. Vector B has a magnitude of 12 m and is oriented 60āˆ˜ to the left of the y axis.? Part 1: Find the magnitude ...
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2answers
58 views

The Vectors in $v=f\lambda$

We are learning about waves in physics and I was just wondering what are the vectors and what are the scalars in this function:$$v=f\lambda$$ I know the velocity $v$ is a vector so that means that: ...
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2answers
24 views

Why use vectors to describe velocity/force/etc instead of treating magnitude and direction as separate values?

I'm only 4 weeks into my first college-level physics course, so this is a very elementary question. Also, in asking this question, I'm just playing devil's advocate in order to better understand the ...
0
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1answer
27 views

Find the magnitude of the resultant force which these engines exert on the rocket?

A rocket fires two engines simultaneously. One produces a thrust of 760N directly forward while the other gives a thrust of 484N at an angle 34.0 degrees above the forward direction. What is the ...
-1
votes
1answer
24 views

Vectors finding direction include the difference between “north of east” and “east of north”

In what direction is your friend from the starting point after skiing 3 km east and then 1.5 km north? so far I know that angle= tan-1(opp/adj)=(1.5/3.0) angle= ...
0
votes
1answer
43 views

Vector Addition and Gravitational Forces [closed]

I was given the following question in my Physics class :- Four particles of masses m, 2m, 3m and 4m are kept in sequence at the corners of a square of side a. What will be the magnitude of the ...
10
votes
4answers
262 views

Basis independence in Quantum Mechanics

The idea that the state of a system does not depend on the basis that we choose to represent it in, has always puzzled me. Physically I can imagine that the basis ought to just yield an equivalent ...
0
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0answers
37 views

Direction of a rectangular vector in two dimensions [closed]

Assuming the following position vector; R(t) = (2+.4t^2)i + (1.0t)j The function provided yields a parabola, how can I find the specific point in which the angle for the position vector evaluated in ...
0
votes
1answer
42 views

Path of a swinging object on a rope [closed]

With my lanyard in hand (weighted by my keys), a gentle swinging motion will put the keys in pendulum motion, swinging back and forth. Pendulum motion is relatively easy to model since it is ...
1
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0answers
32 views

Geometric meaning of negative triple product [migrated]

Create a tetrahedron with corners $A=(1,2,4)$, $B = (1,0,2)$, $C = (2,1,3)$ and $D = (4,1,1)$. Determine the angle $\alpha$ between the edge $AB$ and the side $BCD$. The first step I make is ...
2
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2answers
87 views

Can an angle be defined as a vector?

In Classical Mechanics angular velocity, angular acceleration, torque and angular momentum can be defined as vectors with clear advantages such as the possibility to use vector product to simplify ...
-1
votes
1answer
45 views

Finding angle between two displacements [closed]

Consider two displacements, one of magnitude 6 m and another of magnitude 8 m. What angle between the directions of this two displacements give a resultant displacement of magnitude (a) 14 m, (b) 2 m, ...
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4answers
74 views

When writing a differential equation, when do you take $+\text{d}x$ and when do you take $-\text{d}x$?

When writing a differential equation I'm confused as to when to write $+\text{d}x$ a and when to write $-\text{d}x$ a where $x$ represents some quantity. For example, I wanted to derive the equation ...
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0answers
40 views

What is the meaning of “closure is lost” for a set of kets (or any members of a vector space)?

This is the closure relation in Quantum Mechanics: $$\sum_i |i\rangle \langle i| = 1 $$ which I understand as "the sum of the projections onto the basis vectors leaves the projected vector ...
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0answers
27 views

How to find tangential and normal unit vector to a trajectory from the equation?

Considering a 2D motion in a plane and the equation of the trajectory of a point $y=f(x)$, I don't understand how exactly $\frac{\mathrm{d}y}{\mathrm{d}x}$ can be used. In particular if I'm looking ...
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0answers
14 views

Relations between unit vectors in polar and curvilinear coordinates

I'm a bit confused about the relations between unit vectors in curvilinear and polar coordinates in a plane. Let $u_{R}$ be the radial unit vector in polar coordinates and $u_{N}$ the normal unit ...
-4
votes
1answer
26 views

what is the work done if force F= 3xyi-y^2 moves a particle in the xy plane from (0,0) to(1,2) along the parabola y=2x^2? [closed]

I know that work W=F.dl. But how can i apply this in above question? HOW CAN I FIND dl from the above question?
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1answer
60 views

Dot product and divergence [closed]

Divergence is represented by dot product. How is the divergence related to dot product? And curl is represented by cross product. How is the curl related to cross product?
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2answers
53 views

Time dependent ODE involving cross product

Let $\vec{A}$ be any time dependent vector quantity, and $\vec{\alpha}$ any constant vector. I was told that a solution to the differential equation $$ \dot{\vec{A}} = \vec{\alpha}\times\vec{A} $$ is ...
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3answers
59 views

How to apply a force vector to a position vector?

A particle is present in the two dimensional space. It's position is given by the vector: $$x = \begin{pmatrix} |x| \cos(\theta) \\ |x| \sin(\theta) \end{pmatrix}$$ It experiences a force of: $$ F = ...
-1
votes
1answer
35 views

Two strings in static equilibrium. Why not use the pythagorean theorem to combine vectors? [closed]

I have been working through a physics course and came across the problem: two strings holding a weight in static equilibrium. It all made sense, except for this: Why don't you use pythagorean theorem ...
0
votes
1answer
63 views

How should speed be expressed in Frenet-Serret frame of reference? [closed]

I'm looking for the equation of motion of the ball on a vertical plane with a cylindrical profile. I guess that means I have to use the frame of reference of Frenet-Serret here. Why is the speed of ...
1
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0answers
46 views

Defining a room that is equally lit at every point

Imagine you were in a room designed such that no matter where in the room you stand, a sphere of volume 1 liter held at 2 meters above the ground would be exposed to the same amount of light. How ...
1
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2answers
84 views

Understanding Tensor-operations, covariance, contravariance, … in the context of Special Relativity

I'm currently learning about special relativity but I'm having a really hard time grasping the Tensor-operations. Let's take the Minkowski scalar product of 2 four-vectors: $$\pmb U . \pmb V = ...
1
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2answers
94 views

Two different formulas

My problem is simple : given a particle of mass $m$, charge $q$ and velocity $\bf{v}$. If $\bf{A}$ denotes the magnetic potential satisfying $\bf{B}= \nabla \times \bf{A}$. I want to etablish the ...
1
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0answers
24 views

How does a bikerider turn by leaning on one side? [duplicate]

I am trying to understand the following image: Could someone please help me understnding it. What I understood so far: Your angular velocity mutyplied by the impulse gives you the impulsemoment. By ...
-1
votes
1answer
39 views

Unit Vector Displacement [closed]

A particle starts from the origin at $t = 0$ with a velocity of $+4.0\mathbf{j} \text{ m/s}$ and moves in the $xy$ plane with a constant acceleration of $(6.0\mathbf{i} + 4.0\mathbf{j}) \text{ ...
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1answer
26 views

Why direction of angular velocity is taken along the rotational axis?

I read that it is a convention. But what does that mean in physics? If it would have been a sign assigning matter, I could confess but what convention means here? When we decide the direction of ...
-2
votes
2answers
39 views

vector addition - resultant of two vectors [closed]

Suppose two ships are moving in different directions at some angle between them and we have to find the distance between them we use the formula$R^2=a^2+b^2-2ab\cos\theta$ But if we have to find the ...
0
votes
1answer
69 views

Bounced ray angle of normal direction? (SOLVED) [closed]

TL;DR whats the position of C. I'm currently programming something and for some reason I having problem figuring this one out, imagine having a ray / or ball bouncing (without mass or gravity etc) ...
1
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0answers
33 views

The correct vector equation [closed]

While preparing for the upcoming final physics exam, i encountered the problem on picture below. So, i now that it is not a) and c) since in a) and c) they will have different direction. But i have ...
-2
votes
1answer
45 views

Mnemonic for vector cross versus dot? [closed]

I'm always stuck to remember the difference between vector multiplication with dot product versus cross product? Is there any mnemonic so that I can easily remember which is which?
3
votes
1answer
79 views

What is the difference between scalar and vector mesons?

My understanding is that vectors and pseudooscalars change sign under parity operation and pseudovectors and scalars do not. However, I don't understand what the difference between a vector and ...
3
votes
2answers
63 views

Heuristic explanation of the difference between vectors and scalars in physics

I'm trying to give a student a (physically) intuitive, heuristic explanation as to why certain quantities are vectors and others are scalars. Here is what I have come up with: Scalars are quantities ...
0
votes
1answer
35 views

New direction vector after collision of spheres [closed]

I have a volume in 3-space in which random spheres are spawned in motion. They have the following attributes to them: position known (in three axes) a direction vector (in three axes) a scalar speed ...
1
vote
1answer
44 views

Dropping objects on a rotating disc: angular momentum?

I'm designing a very simplistic particle simulator. Particles are dropped on a spinning disc and then bounce back (although lose some momentum due to the friction of the disc). I'm working with an ...
0
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2answers
27 views

Nature of Pressure

Pressure is defined as force per unit area. Therefore, pressure = force divided by area. Since force and area are both vectors, how can we perform this division without violating the rule of vectors? ...
0
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3answers
83 views

Can we find a vector if its dot product and cross product with another vector is given?

If I have two vectors $\vec{b}$ and $\vec{v}$, and I know that $$ \vec{b} \times \vec{v} = \vec{c} $$ and $$ \vec{b}\cdot\vec{v} = \lambda $$ can I find the $\vec{v}$ vector in terms of the $\vec{c}$ ...
0
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1answer
43 views

Why trajectories approach to origin tangent to the slower direction?

I am reading non-linear dynamics from Strogartz. Suppose, I have two solutions of a non linear system: $x(t) = x_0e^{at}$ and $y(t) = y_0e^{-t}$, where $a\in \mathbb{R}$. Now it is clear that,for ...
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0answers
19 views

what is significance of direction of vector product(torque & angular momentum)?how can one use them practically? [duplicate]

since i came across vector product or cross product i have one doubt that is what direction of torque shows.the direction of product is along axis of rotation(+ve or -ve).is there is any practical use ...
0
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1answer
49 views

Cumulative distance formula

I am working with position recordings over time. Basically, I record the position of animals in a treadmill. They can go forwards or backwards. Hence, position can increase or decrease. However, I am ...
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0answers
40 views

Calculus/Vector Calculus and so on in special relativity book recommandation

I want to learn calculus 1,2,3 vector calculus, analysis and so on in special relativity. But I never found a good and clear book/source on it. Can someone recommend an easy book or internet source on ...
1
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0answers
35 views

What does 'vector-like' mean?

What are properties of vector-like field/particle? What's the counterpart of it? Chiral like?