Vector Definition and 1000 Threads

A force F = -K(yi + xj) (K is a positive constant) acts on a particle moving in the x-y plane. Starting from the origin, the particle is taken along the positive x-axis to the point (a, 0) and then parallel to the y-axis to the point (a, a). What is the total work done by the force F on the...

Homework Statement Homework EquationsThe Attempt at a Solution [/B] A) Mean velocity is defined as <v> = total distance traveled/ total time taken = πR/Γ = 0.5 m/s B) How is part a) different from part b)? I think what Irodov means by mean velocity is mean speed in part a. It is mean...

I have posted this in University linear algebra, but it is possible there is a simple answer for this and the the problem belongs in some other forum. I apologize if that is the case. I am starting with 3 points in 3 space, along with the centroid of the full data set. The data is in principle...

Homework Statement Homework Equations The equation has already been given in the question. The Attempt at a Solution So what I did was find r'(t), r"(t), v(t), v'(t) and plug it into the equation. I've done 3 different full pages of this and have gotten 3 different answers. I'm guessing due...

Hi, In next semester, I am going to take vector calculus. Here is the course description: Vector fields, line and surface integrals, Green's Theorem, Stokes' Theorem, Divergence Theorem and advanced topics such as differential forms or applications to mechanics, fluid mechanics, or...

What is actually the unit normal vector of a surface? Is it this? Or this one? I see that those are opposite in direction. But, I want the correct one, which means that it should point outward. So, which one is correct?

Hi, I would like to ask you how to properly describe the Feynman diagram of the Vector Boson Fusion where the Higgs boson is produced. Two quarks scatters two vector bosons (that means boson W or Z) at some moment which influence each other and produce the Higgs boson. Is that right...

I need help with 2.43 Is there any way to solve 2.43 without drawing the diagram again? And if I must draw another diagram, will I have to guess and check the length of the vectors since all the vectors are equal?

Homework Statement : [/B] r vector = 3t i + (4t-5t2)j. Find the angle made by the vector with respect to the x-axis and the y-axis. 2. Homework Equations : A.B=AxBx+AyBy 3. The Attempt at a Solution : I tried to take the dot product of the unit vector along x-axis and r. I did the same...

In the 1930s, John von Neumann consolidated ideas from Bohr, Heisenberg and Schrodinger and placed the new quantum theory in Hilbert space. In Hilbert space, a vector represents the Schrodinger wave function. I know they are equivalent.. But can we say it is more natural and intuitive to say...

I am confused why is space over field ##R## not over field ##C## ? The entries in each vector is an element of ##\Bbb C## not ##\Bbb R##.

Homework Statement A cricketer throws a 147g ball by exerting a force of 7.5N for 0.84s. If the launch angle is 39 degrees from horizontal, calculate the range of the ball. Homework EquationsThe Attempt at a Solution I have the range equation and I just need to find the magnitude of the...

Homework Statement Ex. 2. Express each of the following by an equation: (a) Two vectors A and B are parallel. (b) Three vectors A, B and C are co-planar. Homework Equations C = A + B 3. The Attempt at a Solution I understand (a) the answer being B = (alpha)*A because that is a scalar...

I am asking this because ∇ is also considered as a vector in some cases. Considering it as a vector in this case ,too, ( ∇× E).E = (- ∂ B/∂t).E = - ∂ (B.E)/∂t =0 Since B and E could be arbitrarily dependent on t, B.E = 0 where B and E are magnetic and electric fields respectively. This...

Homework Statement Suppose the position of an object is given by r⃗ = (3.0t2i^ - 6.0t3j^)m. Where t in seconds. Determine r⃗ at time t = 2.5 s. Express your answer using two significant figures. Express your answer in terms of the unit vectors i^ and j^. Homework Equations plugging in 2.5...

Homework Statement : [/B]Determine the resultant of three vectors of magnitude 1, 2 and 3 whose directions are those of sides of an equilateral triangle taken in order.Homework Equations : [/B] R2 = A2 + B2 + 2 A B cos θ tan α = B sin θ/(A+B cos θ) The Attempt at a Solution :[/B]...

Homework Statement Here are the three problems that i couldn't solve from the book Calculus volume 2 by apostol 10.9 Exercise 2. Find the amount of work done by the force f(x,y)=(x^2-y^2)i+2xyj in moving a particle (in a counter clockwise direction) once around the square bounded by the...

I have to do a teaching assistant job on a multivariable calculus class, I have to survey books that can be useful as resources. Has anyone used this book by Bourne and Kendall? I noticed that the treatment of vector analysis seems good and the chapter on Cartesian tensors seem to be a good...

Im learning about how to find the x and y components of a vector, but I wanted to verify if I'm on the right track.. Ax=A cos(\theta) <-- solving for x Ay=A sin(\theta) <-- solving for y So if a vector is 9.55m long and points in a -48.0 degree direction. Is it Ay= 9.55 sin(-48.0)=7.3

Homework Statement Show that the normal derivative of the coulomb gauge vector suffers a jump discontinuity at a surface endowed with a current density K(\vec r_s ) Homework Equations The vector potential A is given by: A=\frac{\mu_0}{4\pi}\int{\frac{J(x')}{|x-x'|}d^3x} The magnetic...

Hi. I was investigating through this week why there are the differential forms, why are they anti-symmetric, why do we have the Jacobian when expressing the volume in a different coordinate system. This was just fantastic! I found all the connections between these topics. And I found that all of...

Why is the dot product equivalent to the matrix multiplication of its components? I've seen some proofs using Pythagorean and cosine law but they don't give you an intuitive feel as to why matrix multiplication works. The geometric definition (##ab cosθ##) is very easy to understand. To a...

Homework Statement Let L1 be the tangent line to r(t) at the point t = a and let L2 be the tangent line where t = b. Find the equation of the lines L1. Find the equation of the lines L1 and L2 and find the points of intersection. r(t) = <f(t), g(t), h(t)> *bolded letters are vectors Homework...

Hello! I read this definition of vectors in my GR book: "To each point p in spacetime we associate the set of all possible vectors located at that point; this set is known as the tangent space at p, or ##T_p##". This means that each point in space time is viewed as the origin for the 4...

I'm working on a school project and my goal is to recognize objects. I started with taking pictures, applying various filters and doing boundary tracing. Fourier descriptors are to high for me, so I started approximating polygons from my List of Points. Now I have to match those polygons, which...

Homework Statement (Picture attached) Question 1: The system starts at rest. Block a accelerates towards the bottom the the rod. Find the velocity of the block when it is at the bottom of the rod using the "vector method". So this was my midterm question today. I knew how to figure out how...

Hi guys, I am a little confused on the difference between an Algebra and a vector space. I´m guessing there´s a fairly simple distinction. Any guidance would be much appreciated, I accept both hand wavy and hardcore axiom based responses :) Cheers

1. There is a function f(x). Write regulations for it if: -you move it by a vector r=(a,b), -you mirror it over x or y axis.2. f(x) isn't exactly given. Vector is r(a,b).3. If we move it by vector: f(x-a)+b, If we mirror it over x: -f(x) If we mirror it over y: f(-x) So if I am correct...

Relations between vectors in cylindrical and Cartesian coordinate systems are given by \vec{e}_{\rho}=\cos \varphi \vec{e}_x+\sin \varphi \vec{e}_y \vec{e}_{\varphi}=-\sin \varphi \vec{e}_x+\cos \varphi \vec{e}_y \vec{e}_z=\vec{e}_z We can write this in form \begin{bmatrix}...

Homework Statement Two spheres, with 0.5g each, are hanging by 30cm threads, tied on the same spot. The same electric charge is communicated to each sphere; in consequence, the threads move apart until they are about 60^\circ from each other. What is the value of the charge? \theta =...

Homework Statement Find the general solution to the equation: ##{u}\times{(i+4j)}=3k## Homework Equations ##u=(ai+bj+ck)## The Attempt at a Solution I am having trouble visualising what to do here. So my throught so far is that, if i do ##(ai+bj+ck)\times {(i+4j)}=(0i-0j+(4a-b)k) ## now if I...

<Mentor's note: moved from general mathematics to homework. Thus no template.> Prove subspace is only a subset of vector space but not a vector space itself. Even a subspace follows closed under addition or closed under multiplication,however it is not necessary to follow other 8 axioms in...

L1 [x,y]=[2,1]+r[-5,1] L2 [x,y]=[1,4]+s[2,1] L3 [x,y]=[3,5]+t[4,-5] These three lines are sides of a triangle find: 1)the perimeter of the triangle 2) The largest angle 3) the centroid of the triangle so I converted the vector equations into parametric, and then made two of the x parametric...

Homework Statement Hi guys, I have am having a problem with the questions below. what do they mean by show ## B_{perp}=B sin\theta ## I mean I know it a silly question, and my first thought is just use socahtoa, or am I missing something. The question from there on is straight forward...

There is a problem in my Physics textbook which says: Homework Statement "A car runs counter-clockwise in a circular lane of 1 km of diameter, going through the south extreme at 60 km/h on the instant t = 0. From that point onwards, the driver accelerates the car uniformely, reaching 240 km/h...

Excuse me if this is a bad question but: Does ##d P_x d P_y = d^2 \vec P ##? I thought not because ##P_x ## is a scalar , a component of the vector, whereas ##\vec P ## is a vector? Thanks in advance

Hello, I am trying to understand how vector images are formed and manage to be scaled up or down without distortion. Bitmap images are easy: they are a grid of pixels and each pixel has a certain color. Scaling a bitmap image of 10x10 pixels implies adding new extra pixels and using...

Homework Statement http://imgur.com/a/k7fwG Find the vector magnetic potential at point P1. Homework Equations Vector magnetic potential given by: $$ d \bar{A} = \frac{\mu I d\bar{l'}}{4 \pi | \bar{r} - \bar{r'} | } $$ The Attempt at a Solution I split up the problem in 3 parts, first...

1. Problem ##g_{uv}'=g_{uv}+\nabla_v C_u+\nabla_u C_v## If ##g_{uv}' ## is given by ##ds^2=dx^2+2\epsilon f'(y) dx dy + dy^2## And ##g_{uv}## is given by ##ds^2=dx^2+dy^2##, Show that ## C_u=2\epsilon(f(y),0)##? Homework Equations Since we are in flatspace we have ##g_{uv}'=g_{uv}+\partial_v...

[ Moderator note- Edited to re-insert formatting template headers] Hi guys, I am stuck at this problem, Homework Statement Here it is given that an insulating sphere of radius a, carries a charge density ρ=ρ'( a^2-r^2)cosθ, when r <a. How will the leading order term for the electric field at...

Hi, hopefully a quick question here...how do you calculate the angle between two vectors if the only information you have is the value of their scalar product and the magnitude of their cross product? Thanks! Andy

I've been racking my brain for a while now over what I feel should be a simple problem to solve, but my answer is wrong. I'm not wildly wrong, but wrong enough to think I've made a proper error and it's not just a rounding error or something. The question goes like this: A dog in an open field...

hello every one can one please construct for me left invariant vector field of so(3) rotational algebra using Euler angles ( coordinates ) by using the push-forward of left invariant vector field ? iv'e been searching for a method for over a month , but i did not find any well defined method...

To me the state vector represents the following... 1) The number of elements in the state vector is the number of possible outcomes. Call that number n. 2) The value of each element in the state vector is the probability amplitude associated with that outcome. If that is true, then it seems to...

Homework Statement A bullet was shot at 40m/s Elevation angle : 37° Bullet mass = 0.01 Kg Question : how much work is done by the force of gravity to the bullet since it was shot until it reaches the ground again Homework Equations mgh = E.Pot 1/2mv ^2 = E kinetic The Attempt at a Solution...

Hello, I have a question about why I can't determine the angle between two vectors using their cross product. Say there are two vectors in the XY-plane that we want to find the angle between: A = -2.00i + 6.00j B = 2.00i - 3.00j The method to do this would be to work out the scalar product of...

Homework Statement [/B] Let f and g be scalar functions of position. Show that: \nabla f \cdot \nabla(\nabla ^2 g)-\nabla g \cdot \nabla(\nabla ^2f) Can be written as the divergence of some vector function given in terms of f and g. Homework Equations [/B] All the identities given at...

Let $a, b \in \Bbb R$ and $u, v \in \Bbb R^2$, with $u = (0, 1)$ and $v = (1, 0)$. Show that every vector in $\Bbb R^2$ is of the form $au + bv$. Under what conditions is this true for general vectors $u = (u_1, u_2)$ and $v = (v_1, v_2)$? No idea where to begin. Would appreciate any help.

Homework Statement Homework Equations RAO = b(Sinβj+Cosβk) The Attempt at a Solution [/B] The box in red is ω. However I am unsure of where they got the box in blue from? As mentioned above, RAO = b(Sinβj+Cosβk) so not sure where they got the box in blue from? I know of the vector triple...

There are two charges with charge q and mass m and they are in equilibrium. Then, in the diagram why is my teacher saying that electrostatic force(F)=mg? Below is diagram.