Geometric object with magnitude (length) and direction.

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1answer
52 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
44 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 ...
-1
votes
1answer
14 views

Problem in solving numericals involving vectors [on hold]

I am having trouble solving numericals involving vectors. Where do I learn the basics?
1
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3answers
347 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 ...
-3
votes
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
15 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
3answers
121 views

Vector decomposition validity

Is force or field decomposition into component vectors always valid? Lets say a constant electric field $\vec{F}$ is acting in space such that it makes an angle $\phi$ with respect to the horizontal ...
1
vote
1answer
484 views

Relative wind velocity explanation - understanding Irodov problem 1.6

I am having trouble understanding the reasoning behind the solution in this Irodov General Physics problem. The problem is 1.6: 1.6. A ship moves along the equator to the east with velocity vo = ...
0
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4answers
125 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 ...
-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
3answers
105 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.
2
votes
2answers
6k views

Derive vector gradient in spherical coordinates from first principles

Trying to understand where the $\frac{1}{r sin(\theta)}$ and $1/r$ bits come in the definition of gradient. I've derived the spherical unit vectors but now I don't understand how to transform ...
1
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2answers
334 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 ...
-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 : ...
3
votes
1answer
272 views

Rolling a ball into a cone; what should the forces overall be?

This is my solution to finding angular displacement/velocity/acceleration on cone so far. Consider a cone, with an apex of half-angle $\psi$ pointing down, and a height of $h$. If I roll a ball into ...
0
votes
3answers
148 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 ...
4
votes
4answers
217 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 ...
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}} ...
1
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3answers
401 views

Why does the moment of force (aka. torque) depend on the perpendicular distance?

Couyld anyone explain how the lecturer concluded that $$(\underline{r_2} - \underline{r_1}) \times \underline{H} = \underline{p} \times \underline{H}$$
-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 = ...
1
vote
1answer
214 views

General definition of vector, spinor, and spin

I am looking for basic and exact definitions of fundamental physical concepts in graduate level. I reach this following definitions. Could you please help to improve these definitions. Spin: ...
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votes
2answers
57 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 ...
1
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3answers
79 views

Find time-parametrization given path and speed of a particle

Consider a particle in two dimensions with position vector $r(t)=<x(t),y(t)>$ and the shape of the path is described by a function $y(t)=f(x(t))$ (Thus $r(t)$ is a parametrization of $f$ with ...
2
votes
1answer
2k views

Laws of addition of Vectors

How Triangle Law and Parallelogram law of addition of Vectors are different?Ain't they. Please don't tell me the things written in book......give me the appropriate reason.And how do i distinguish ...
0
votes
1answer
51 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
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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 ...
0
votes
2answers
351 views

Relative motion. Setting course of closest approach

Let $r_{P/Q}$ be the position vector of $\overrightarrow P$ relative to vector $\overrightarrow Q$ and $v_{P/Q}$ the velocity vector of $\overrightarrow P$ relative to $\overrightarrow Q$. Suppose ...
0
votes
3answers
154 views

Animating an Acceleration Vector - Acceleration of object on a crested path in gravitational field

So I was reading in Chapter 3 of my textbook, Sears & Zemanksky's University Physics with Modern Physics by Young and Freedman, 13th Edition, and the discussion took us to a definition of the ...
1
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0answers
27 views

Write the force as a sum [closed]

We suppose that a force $\overrightarrow{F}$ (for example, the gravity) is applied vertically downwards to an object that is placed at a plane which has an angle of $45^{\circ}$ with the horizantal ...
-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
114 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 ...
12
votes
7answers
2k views

Quaternions and 4-vectors

I recently realised that quaternions could be used to write intervals or norms of vectors in special relativity: $$(t,ix,jy,kz)^2 = t^2 + (ix)^2 + (jy)^2 + (kz)^2 = t^2 - x^2 - y^2 - z^2$$ Is it ...
20
votes
8answers
2k views

Is it foolish to distinguish between covariant and contravariant vectors?

A vector space is a set whose elements satisfy certain axioms. Now there are physical entities that satisfy these properties, which may not be arrows. A co-ordinate transformation is linear map from a ...
2
votes
3answers
232 views

Dimension of vector resulting from tensorial product

I'm quoting what I found in a book about quantum computation: Individual state spaces of $n$ particles combine quantum mechanically through the tensor product. If $X$ and $Y$ are vectors, then ...
1
vote
2answers
310 views

Point charge potential (sign problem)

I'm a bit embarrassed, but I'm not able to compute the electric potential at point $P$ (at a distance $R$ from the origin) generated by a positive unitary point charge in the origin with the right ...
1
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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
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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 ...
4
votes
3answers
707 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. ...
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 ...
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
41 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
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 ...
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\ ? ...
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 ...