Vector Definition and 1000 Threads

Homework Statement "A bird flew 40 m to the west, then 100 m in a direction 36.9 degrees to the north of east. Use the algebraic addition of vectors to fins the magnitude of the bird's net displacement" Use sin (36.9) =0.6 and cos (36.9) = 0.8 Homework Equations Vector addition? A =...

Why are the resultant's X and Y components of two forces equal the sum of the X and Y components of the two forces?

Homework Statement Three vectors are given: A=2i+3j, B=1i+5j, C=-1i+3j Find constants x and y such that xA+yB=C Homework Equations N/A The Attempt at a Solution The form of the final equation reminded me if standard form of a slope, so I found the total vector for A,B, and C. I was then going...

When doing integration such as \int_{0}^{2\pi} \hat{\rho} d\phi which would give us 2\pi \hat{\rho} , must we decompose \hat{ρ} into sin(\phi) \hat{i} + cos(\phi) \hat{j} , then \int_{0}^{2\pi} (sin(\phi) \hat{i} + cos(\phi)\hat{j}) d\phi , which would give us 0 instead? Thanks

Homework Statement Givens: An object with a mass of 2kg has a momentum of p=<-1,-2,3>. The first two questions asked for the magnitude of the momentum and the corresponding unit vector, which i found to be 3.74 and <-0.267,-0.535,0.802> respectively. The next question asks for the speed of the...

Homework Statement Vectors A and B have equal magnitudes of 4.93. If the sum of A and B is the vector 6.79j, determine the angle between A and B Homework Equations c^2 = a^2 + b^2 -2abcos(theta) The Attempt at a Solution I just rearranged the formula above so that I could solve for the...

I have this odd difficulty when it comes to vector calculus. No matter what I do, seeing these equations just stays daunting. Its a massive effort for me to read them, and when I say "read" I mean look at the equations, and actually understand what it is it wants me to do. Now as with most math...

Homework Statement Two vectors A and B have precisely equal magnitudes. For the magnitude of A + B to be 65 times greater than the magnitude of A - B, what must be the angle between them? Homework EquationsThe Attempt at a Solution I tried using the dot product and solving for the angle but i...

Homework Statement r1= 2 7 r2=-1 -6 Homework Equations A-lambda*I=0 (A-lambda*I)*x=0 The Attempt at a Solution I have got following eigen values: lambda1 = -5 and lambda2=1 A-lambdaI matrix is: r1 = 7 7 r2 = -1 -1 and x matrix is: r1 =x r2 =y I can't understand why we have to use...

What's the difference between saying that a vector's direction is north of east and north east?

I just want to know the difference between those rules: 1. R^2 = F1^2 * F2^2 + 2*F1*F2*COS(the angle between F1 and F2) 2. The second is about the parallelogram rule, it says that the two vectors are added and their summation is the magnitude of the resultant. Which one is correct?

Hello, We defined a k-form on a smooth manifold M as a transfromation Where the right space is the one of the alternating k-linear forms over the tangent space in p. If we suppose we know, that we get a basis of this space by using the wedge-product and a basis of the dual space, then we might...

I have a question regarding the dot product and the cross product differentiation. I was wondering whether: $$\frac{d(\vec{A}.\vec{B})}{du} = \vec{A}. \frac{d\vec{B}}{du} + \frac{d\vec{A}}{du} .\vec{B}$$ is the same as $$\frac{d(\vec{A}.\vec{B})}{du} = \frac{d\vec{A}}{du} .\vec{B} + \vec{A}...

Homework Statement Consider a configuration consisting one +q charge ( upper right) and three −q charges, arranged in a square. Side lengths = d. Calculate the total F force vector acting on charge +q.Homework Equations Vector form of culomb’s force F=( kq1q2/r^2) rhat (rhat for unit...

Homework Statement Problem attached in Dipole.JpgHomework Equations The Attempt at a Solution I am fine with Part A of the problem. I am just trying to understand what part B is asking. Are they asking what is the magnitude and direction of the dipole vector associated with charges q1 and q1 at...

Homework Statement Compute the flux of a vector field ##\vec{v}## through the unit sphere, where $$ \vec{v} = 3xy i + x z^2 j + y^3 k $$ Homework Equations Gauss Law: $$ \int (\nabla \cdot \vec{B}) dV = \int \vec{B} \cdot d\vec{a}$$ The Attempt at a Solution Ok so after applying Gauss Law...

please help as I'm very old but play Pickleball which is similar to tennis but with a plastic whiffle ball and a solid racket on a reduced size modified tennis court. What I'm trying to figure out is the following: a player on the other side of the net and to the left of me returns the ball that...

Hello! (Wave) Let $W$ be the subspace of $\mathbb{R}^3$ that is orthogonal to the vector $w_1=(-1,-1,1)$ and $p=(x,y,z)$ the projection of the vector $v=(-1,1,2)$ onto $W$. What is $7x-11y+5z$ equal to?I have thought the following: $\text{proj}_Wv=\frac{\langle v, w_1\rangle}{\langle w_1...

Homework Statement A vector field is pointed along the z-axis, v → = a/(x^2 + y^2)z . (a) Find the flux of the vector field through a rectangle in the xy-plane between a < x < b and c < y < d . (b) Do the same through a rectangle in the yz-plane between a < z < b and c < y < d . (Leave your...

In the four-observation method of Gauss for orbit determination, the right ascension and declination of an asteroid is observed at specified times, and the heliocentric position of Earth is obtained from tables (or JPL Horizons) for those same times. I can follow the procedure to the point...

How do I calculate the resultant of three component vectors set mutually at 60 degrees to each other (not in the same plane)?

Homework Statement Hi. Its not really a problem but just a general question. When doing graph translations, such as move the parabola x units right or y units up etc, Is it okay to use vector format. So instead of saying move this equation 4 units left, could you write it like this -> <-4,0>...

Homework Statement A force of magnitude 50N is applied at the bottom point Q of a disk of radius 8m that is pinned at P (leftŸmost point) See attached picture (a) Find the angle between the force and the vector from P to Q. (b) Find the magnitude of the applied torque. Homework Equations...

Can we say that a volume element can be represented by a vector, or is there some hidden complication that makes this inadvisable? For some background, the stress-energy tensor has been described as the density of energy and momentum, in for instance MTW. So if one says that the represention...

How to draw the following vector field: F(r) = 1/(r^2) I know the shape of this vector field and how to draw a vector field in terms of x- and y-components, but I was wondering how to draw a vector field in terms of a vector r, as given above, without knowing its components. Any advice is much...

Equation 9.2.25 defines the inner product of two vectors in terms of their components in the same basis. In equation 9.2.32, the basis of ## |V \rangle## is not given. ## |1 \rangle ## and ## |2 \rangle ## themselves form basis vectors. Then how can one calculate ## \langle 1| V \rangle ## ? Do...

Hey, I've got this problem that I'm trying to work out. I've tried a couple of things, but they don't really get me anywhere. Here's the problem Find a vector that spans the line defined by these two equations. $x+6y+3z=0$ $x+3y+4z=0$ What would be the best way to go about this? Thanks :)

Hi PF! Given a vector field ##\vec f## in spherical coordinates as a function of a single parameter ##s##, shown here as $$\vec f(s) = f_r(s) \hat r + f_\theta(s) \hat \theta + f_\phi(s) \hat\phi$$ where here subscripts do not denote partial derivatives, but instead are used to define...

Homework Statement https://www.physicsforums.com/attachments/229290 Homework Equations The Attempt at a Solution I am not sure what equation to use for the volume[/B]

Homework Statement f f Homework Equations ##a = {v^2}{r}## ##d = vt## The Attempt at a Solution The way I do it is break it down into the curved and straight segment. The bicycle is always traveling at a constant speed. Curved portion: distance ##\frac{\pi R^2}{4}## acceleration ##=...

Can we find the angle between resultant and one of its vectors without breaking into components?

Homework Statement 1.1.3 1) Do functions that vanish at the endpoints x=0 and L=0 form a vector space? 2) How about periodic functions? obeying f(0)=f(L) ? 3) How about functions that obey f(0)=4 ? If the functions do not qualify, list what go wrong.Homework Equations The Attempt at a...

Homework Statement Homework Equations definition of null vector, [/B] The Attempt at a Solution null vector : ## |0 \rangle = (0,0,0) ## inverse of (a,b,c) = ( - a, -b, -c) vector sum of the two vectors of the same form e.g. (c,d,1) + ( e,f,1) = ( c+e, d+f, 2) does not have the same...

For the vector valud function F in the image, the three components of the output vector at a point are functions of (x,y,z)the three coordinates of the point.But while calculating divergence, why is the rate of change of x component of the output along x direction alone is accounted(similarly...

Would you explain this sentence in detail?

Homework Statement A pilot wishes to fly at maximum speed due north. The plane can fly at 100km/h in still air. A 30km/h wind blows from the south-east. Calculate: a) The direction the plane must head to fly north. b) Its speed relative to the ground. Homework Equations Sine Rule...

So, velocity is a vector, right? And vectors can't have negative magnitudes, right? Then why is leftward velocity considered negative in 1D kinematics? It just seems off to me. Same with acceleration, and pretty much _every vector in all of physics._

The context for the question is in the attachments (pg1.png, pg2.png, pg3.png), so there is some reading involved. Although, it is a short and simple read if anything. The inquiry is in (inquiry.png). My understanding of the situation is that Q(t) abides by the differential equation Q'(t)Q(t)T...

Let me start off by stating a given problem: A baseball is hit, and leaves the bat at a speed of 100 mph and at an angle of 20° from the horizontal. Express this velocity in vector form. So we're given the velocity and the angle at which the ball is hit. The speed corresponds to the vector's...

Hi, Is there a method to represent a known two-dimensional vector field w of two coordinates x and y with zero divergence and non-zero curl as $$ \vec{w}(x,y) = a \nabla b \, , \hspace{4mm} \nabla \cdot \vec{w} = 0 \, , \hspace{4mm} \nabla \times \vec{w} = f(x,y) \, ?$$ How would one proceed to...

I am trying to understand why an accelerating charge emits radiation/electromagnetic waves but a uniformly moving one does not. I saw one video on Youtube where it seemed that it was explained by the fact that with a uniformly moving charge the Poynting vector was pointing 'in to the volume' -...

Hello, I am having trouble comprehending how grids are made and defined in computers. What is the unit that they use and how is it defined ? I know that softwares use standardized units of measure (measurement) such as centimetre. Basically, how is a 3-Dimensional Space created in computers...

Hello. I'm currently entering into a Physics II class at the start of my third semester at UCONN (my first semester was introductory modern physics - kinetic theory, hard-sphere atoms, electricity and magnetism, scattering, special relativity, Bohr model, etc), and finished Physics I off with...

Hi. I want to normalize a discretized function ##p_{k,k'}##, to satisfy simultaneously two conditions. The normalized function ##p^*_{k,k'}## has to satisfy simultaneously: 1) ##\sum_{k=1}^{M} p^*_{k,k'} w_k=1##, for all ##k'=1,2,...,M##; 2) ##\sum_{k=1}^{M} p^*_{k,k'} w_k \hat \Omega_k \cdot...

Hello PF, I was reading Carroll’s definition of the commutator of two vector fields in “Spacetime and Geometry”, and I’m having (I think) a simple case of notational confusion. He says for two vector fields, ##X## and ##Y##, their commutator can be defined by its action on a scalar function...

Homework Statement For a left invariant vector field γ(t) = exp(tv). For a gauge transformation t -> t(xμ). Intuitively, what happens to the LIVF in the latter case? Is it just displaced to a different point in spacetime or something else? Homework EquationsThe Attempt at a Solution

Homework Statement Homework Equations Is my solution correct? If not then please point out the mistakes and help me solve this question in the right way. Thanks in advance. The Attempt at a Solution

Disclaimer: I am not a physicist, just trying to learn some parts of it in my free time. And I do not mean to propose any kind of "new-theory" with my question. I always thought that Maxwell equations in their differential form for B and E may be reformulated/updated to include a magnetic...

f(\vec{x}+\epsilon \vec{y})-f(\vec{x})=\epsilon \mbox{d}f_{\vec{x}}(\vec{y})+O(\epsilon^2). Is ##\mbox{d}f_{\vec{x}}(\vec{y})## dual vector and why? Is it because ##\mbox{d}## is linear transformation? Also why equality f(\vec{x}+\epsilon \vec{y})-f(\vec{x})=\epsilon...

Hi there I'm having a hard time trying to understand how come ∂r^/∂Φ = Φ^ ,∂Φ/∂Φ = -r^ -> these 2 are properties that lead to general formula. I've been thinking about it and I couldn't explain it. I understand every step of "how to get Divergence of a vector function in Cylindrical...