Geometric object with magnitude (length) and direction.

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1answer
22 views

Vectors and projectile [on hold]

Two particles A and B starts moving from a high point O at t=0 in the opposite direction with horizontal velocities 9 3 m/s and 4 m/s respectively. Due to earth's gravitational field the two particles ...
-1
votes
0answers
14 views

Projections of a vector [on hold]

The projections of a vector on x-y plane, the y-z plane and the z-x plane are √13,√40,√45 respectively. The vector lies on the first octant. It's approximate magnitude is
-2
votes
0answers
75 views

What does cross product mean in simple words? [migrated]

Two numbers 3 and 4 their multiplication is each one from the first number is repeated a number of times as the second number i.e. 3 times 4 is (1+1+1) times four meaning 1+1+1+1 + 1+1+1+1 + 1+1+1+1 ...
0
votes
4answers
120 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
98 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.
-1
votes
2answers
31 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
votes
3answers
147 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
70 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
votes
2answers
45 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
214 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
36 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
56 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
50 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: ...
0
votes
0answers
16 views

How do I evaluate this general magnetic dipole equation for this given setup?

This shouldn't be too hard a question (mostly focused on vector multiplication) but I'm still not confident in my answer. Basically, I am looking at the force between two magnetic dipoles and using ...
-1
votes
0answers
38 views

Prove that any vector can be written as the sum of any three non-coplanar vectors [migrated]

I'm trying to prove the above in the following form: $ \boldsymbol{V} = (\boldsymbol{V} \centerdot \boldsymbol{a}^1)\boldsymbol{a}_1 + (\boldsymbol{V} \centerdot \boldsymbol{a}^2)\boldsymbol{a}_2 + ...
1
vote
3answers
140 views

Why do we need both dot product and cross product?

I was looking for an intuitive definition for dot product and cross product. I have found two similar quesitions in SO, but I am not satisfied with the answers. Finally I found a possible answer here. ...
0
votes
2answers
112 views

Cross product and the right hand rule - what is the intuition behind it? [duplicate]

I understand that by convention, the cross product is defined to be the vertical projection of vector $A$ on $B$ in the case of $A \times B$. But the vertical projection of $A$ on $B$ would still be ...
1
vote
0answers
32 views

What is a diffusionless fluid?

I'm taking a course in astrophysical fluid dynamics and have come across a problem involving "small diffusionless disturbances" of a fluid. Based on the nature of the course I expect the examiner to ...
-1
votes
1answer
37 views

Velocity of a car in circular circuit [closed]

Prior apology for any violation of rules and regulation and poor expression of question. Statement: A racing car moves along a circular circuit with a constant speed of $20\text{ms}^{-1}$ in 5 ...
0
votes
0answers
22 views

Can't we assign any other direction for instantaneous angular velocity except along the axis of rotation? [duplicate]

We specify the direction of instantaneous angular velocity using the right hand thumb rule. I just want to know that is it just a matter of convention or we don't have any other direction for it to be ...
1
vote
0answers
39 views

how to rotate scaled-vector (orientation) by scaled-vector (rotation)

Recently I seem to have gotten the physics-engine portion of my 3D simulation/game engine [apparently] working correctly. The most convenient way to store and compute position and orientation are in ...
4
votes
3answers
703 views

Work = Force x Distance vs Displacement

The difference in using Distance vs Displacement is demonstrated in this example: Work = Force x Distance If I carry an object to and fro 10 metres, the work done would be Force x 20 metres. ...
3
votes
3answers
201 views

Notation of vectors

It's very common to see $\text{F} = 30 \text{ N}$ when the problem is unidimensional. Yet, force is a vector. Shouldn't I write $|\overrightarrow{F}| = 30 \text{ N}$? Because if I write ...
2
votes
1answer
40 views

Sign of Gaussian surface that encloses negative charge

I can't solve a contradiction that have appeared in my head. Let's assume we have a negative charge, if we enclose it by a spherical surface and $A$ is surface of the sphere, then we will have ...
-1
votes
3answers
79 views

What is the Vector/Cross Product?

I have decided to start learning physics before I am required to take the class in 11th grade so that I will be ahead of my classmates. I found a cheap physics book on amazon and ordered it but ...
2
votes
1answer
42 views

What's the physical meaning of change in momentum vector?

If I there is a initial momentum of 10Ns upwards, and final momentum of 10Ns to the right, I can find the difference in momentum by drawing a triangle and finding the resultant vector. But, how is ...
2
votes
3answers
178 views

Deriving cross product from angular momentum algebra

Is it possible to derive: \begin{equation} \hat{L}=\hat{r}\times \hat{p} \end{equation} from the angular momentum algebra: \begin{equation} [\hat{L}_i,\hat{L}_j]=i\ \hbar\ \epsilon_{ijk}\hat{L}_k\ ? ...
0
votes
1answer
41 views

Why is parallel component of velocity along position vector considered rate of change of position?

If you have a position vector and a velocity vector of a particle, then the component of velocity vector along position vector is the rate of change of distance of the particle from the reference ...
2
votes
2answers
41 views

what does magnetic field vector mean?

I am trying to understand what a magnetic field vector tells us about the magnetic field. I understood that a vector is just a representation of a point and how much it is moved in x,y and z direction ...
2
votes
2answers
87 views

Making sense out of covariance and contravariance

I just read about co- and contravariant vectors and I am not sure that I got it right: If we imagine that we have a n-dimensional manifold $M$ then a tangent space is spanned by the vectors ...
0
votes
1answer
46 views

Is the flux through A the same as the flux through B?

In the figure below, the amount of field lines through A is the same as the amount of field lines through B, but can you say the flux through A is the same as the flux through B as well?
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votes
1answer
21 views

Calculating uniform angles between 2 vectors [closed]

If I have two vectors, say: [100] and [101] and I want to calculate two angles between them, uniformly distributed, would it just be: [1 0 0.33] and [1 0 0.66]? So, [100] = 0 degrees [101] = 45 ...
1
vote
0answers
28 views

How do I show $e_r$ and its first- and second time derivative?

What does a charge q moving in a circular orbit with a constant velocity (a "rotating charge") and a stationary observer that measures the E field look like? And how do I show $e_r$ and its first- and ...
1
vote
2answers
121 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 ...
0
votes
2answers
44 views

Why taking components of a component of a vector is invalid?

Suppose there's a force $F$ of magnitude 10 newtons in the direction of positive y-axis acting on a particle A. I know that the particle would not experience any force in the positive x-direction ...
1
vote
2answers
39 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 ...
0
votes
2answers
90 views

Direction of electric field lines and electrostatic force

Direction of electric field and electrostatic force should be same by the equation $$\vec{F} = \frac{k q q_0}{r^2}$$ Electric Field $$\vec{E} = \frac{k q}{r^2}$$ Let us suppose that there is a ...
0
votes
2answers
66 views

When does $\mathbf n\times(\nabla V_2-\nabla V_1)=0$ imply $V_1=V_2$

I was reading a paper on electrohydrodynamics which has the following sentence (in my own words): At the interface/boundary, the requirement of continuity of the tangential component of the ...
0
votes
1answer
19 views

How to find one of the vectors when we know the other, the angle between the vectors and the result? [closed]

We're given that the result of the two vectors $a$ and $5$ is $7$ and the angle between the two vectors $5$ and $a$ is $60$ $degrees$. How do we calculate the of the vector $a$ ? I used $R^2 = P^2 + ...
2
votes
1answer
39 views

ϕ-component of equation of moition: proving a relationship [closed]

I have the following velocity vector (in spherical polars): \begin{equation} \textbf{v} = u \hat{\textbf{r}} + v_{\phi}\hat{\boldsymbol\phi} \end{equation} Where $u(r) = u$ and $v_{\phi} (r) = ...
0
votes
1answer
56 views

Resolution of force vectors

For example in a simple pendulum problem.. the forces that act on the bob are tension and gravitational force. but while the resolving the vectors to find T(tension) at any given angle x with the ...
0
votes
3answers
75 views

Tension on a string

A string is attached at both extremities and put under tension $T_0$ at rest. We know that if we pull the string upwards from the middle, the tension will increase. But why is it that, admittedly, ...
1
vote
1answer
130 views

Difference between Speed and Velocity

What is the difference between Speed, Velocity and Acceleration? Could any one describe it pictorially?. I am more over confused even after investigating many times. I am unable to relate myself ...
0
votes
2answers
173 views

Is a vector and a unit vector dimensionless

Lets say I have a position vector $\vec r$. Is it dimensionless or does it have a dimension of length i.e $[L]$. Also does the unit vector $\hat r$ have a dimension?
1
vote
1answer
74 views

Is the Mass flow rate (Mass flux) a scalar quantity?

Wikipedia states that mass flow rate is a scalar quantity, however Mass Flow Rate= Density x Cross Sectional Area x Velocity and velocity is a vector quantity, so this would imply Mass Flow Rate is ...
-1
votes
1answer
89 views

A particle is constrained to move around the unit circle in the xy plane according to (x,y,z) = (cos(t^2),sin(t^2),0) t >= 0 [closed]

A particle is constrained to move around the unit circle in the xy plane according to (x,y,z) = (cos(t^2),sin(t^2),0) t >= 0 At what point should the particle be released to hit a target of (2,0,0)? ...
2
votes
4answers
196 views

Normal Vectors to these Hypersurfaces on a Lorentzian Manifold

With respect to the coordinates $(x^{0},x^{1},x^{2},x^{3})=(v,r,\theta,\phi)$, we have the following components of the metric tensor: $\begin{bmatrix} g_{00} & g_{01} & g_{02} & ...
3
votes
2answers
102 views

Why is the “complete metric space” property of Hilbert spaces needed in quantum mechanics?

I have been learning more about Hilbert spaces in an effort to better understand quantum mechanics. Most of the properties of Hilbert spaces seem useful (e.g. vector space, inner product, complex ...
0
votes
1answer
44 views

How can Bernoullis be solved without Vectors [duplicate]

Some time ago I asked a question why Dynamic pressure is considered scalar. Why is the dynamic pressure not a vector quantity? This still puzzles me so I hope to give a scenario that doesn't make ...
11
votes
7answers
266 views

How can a set of components fail to make up a vector?

Many books in Physics insist to define vectors are objects with components with the property that the components transform in a proper way under a change of coordinates. Now, in mathematics, on the ...