What is Vector: Definition and 1000 Discussions

Homework Statement [/B] The door is held open by the means of 2 chains. If the tension in AB and CD is Fa = 300 N and Fc = 250 N, respectively, express each of these in Cartesian Vector Form Homework Equations Sin / cos / tan The Attempt at a Solution The angle of FA at B is...

Suppose we have defined a vector ##V## at a point ##x##, so it has components ##V^\mu(x)## at ##x##. Let ##y## be another point, such that ##y^\mu = x^\mu + \epsilon \zeta^\mu(x)##, ##\epsilon## a scalar. Now, since ##x## and ##y## are coordinate points, the vector ##V## should not depend on...

hello every one . can someone please find the left invariant vector fields or the generator of SO(2) using Dr. Frederic P. Schuller method ( push-forward,composition of maps and other stuff) Dr Frederic found the left invariant vector fields of SL(2,C) and then translated them to the identity...

Hi (1/sqrt(4t²+1), 2t/sqrt(4t²+1)) gives a unit tangent to the curve y=x^2 at point (t,t^2). Viewing the vector as velocity, shouldn't I be able to integrate it and get a parameterization for y=x^2?

Homework Statement The question is: if vectors v1, v2, v3 belong to a vector space V does it follow that: span (v1, v2, v3) = V span (v1, v2, v3) is a subset of V.[/B] 2. The attempt at a solution: If I understand it correctly the answer to both questions is yes. The first: the linear...

Hey guys, I'm new to the forum and I have a question that has stumped several of the professors at my school. My idea is to use an electric motor with a solid rocket engine on a thrust stand to spin the exit cone. The concept would make use of centripetal force to increase the pressure of...

Homework Statement The surfaces ##x^2+y^2 = 2## and ##y=z## intersect in a curve ##C##. Find a unit tangent vector to the curve ##C## at the point ##(1,1,1)##. Homework EquationsThe Attempt at a Solution So I'm thinking that we can parametrize the surfaces to get a vector for the curve ##C##...

Homework Statement Let a is a complex vector given by a = 2π K - i ρ / α^2 , where ρ is a two dimensional position vector and K is the corresponding two dimensional vector in the Fourier space. In order to find magnitude of this vector, i found that it is 4π^2 K^2 + ρ^2 / α^4 . The logic...

Can anybody give me a list of all cross products in physics. I have the following in my list: Torque $$\vec{\tau}=\vec{F}\times\vec{r}$$ Angular momentum $$\vec{L}=\vec{r}\times\vec{p}$$ Velocity $$\vec{v}=\vec{\omega}\times\vec{r}$$ Biot-Savart law $$\vec{dB}=\dfrac{\vec{i...

δij is the Kronecker delta - is this considered a tensor or vector? I know it means the identity when i=j so I'm going to guess tensor because it's a matrix rather than just a vector but I want to make sure. A matrix is a rank 2 tensor and a vector is a rank 1 and a scalar is a rank 0? How does...

Homework Statement F(x,y,z) = xzi Homework Equations N/A The Attempt at a Solution I just said that x = rcos(θ) so F(r,θ,z) = rcos(θ)z. Is this correct? Beaucse I am also asked to find curl of F in Cartesian coordinates and compare to curl of F in cylindrical coordinates. For Curl of F in...

Homework Statement Consider the set V + {all periodic *complex* functions of time t with period 1} Draw two example functions that belong to V. Show that if f(t) and g(t) are members of V then so is f(t) + g(t)Homework EquationsThe Attempt at a Solution f(t) = e(i*w0*t)) g(t) =e(i*w0*t...

Homework Statement Let v(0) = [0.5 0.5 0.5 0.5]T, v(1) = [0.5 0.5 -0.5 -0.5]T, v(2) = [0.5 -0.5 0.5 -0.5]T, and z = [-0.5 0.5 0.5 1.5]T. a) How many v(3) can we find to make {v(0), v(1), v(2), v(3)} a fully orthogonal basis? b) What are z's coefficients of expansion αk in the basis found in...

Homework Statement The texts are taken from http://ingforum.haninge.kth.se/armin/fluid/exer/deriv_navier_stokes.pdf and https://simple.wikipedia.org/wiki/Stress_(mechanics)Homework EquationsThe Attempt at a Solution The formula for stress is ##\sigma=\frac{F}{A}## (I). From the document...

Homework Statement Find the unit vector perpendicular to the level curve of f(x,y) = x2y-10xy-9y2 at (2,-1) Homework Equations Gradient The Attempt at a Solution I'm not sure what it's asking. Wouldn't this just be the gradient of f(x,y) evaluated at (2,-1) then normalized? or am I missing...

Homework Statement Provide a complete proof that a regular plane curve γ : I → R2 can near each point γ(t0) be written as a graph over the tangent line: more precisely, there exists a smooth real valued map x → f(x) for small x with f(0) = 0 so that x → xT(t0) + f(x)JT(t0) parametrizes γ near...

Homework Statement The electric potential at points in an xy plane is given by V = (1.5 V/m2)x2 -(2.9 V/m2)y2. What are (a) the magnitude of the electric field at the point (3.9 m, 2.9 m) and (b) the angle that the field there makes with the positive x direction. Homework EquationsThe Attempt...

Okay so when there is time-translation symmetry because the metric components do not have any time- dependence, ##\partial_x^0## is a Killing vector. I'm just confused what this means explicitly, since a derivative doesn't make sense without acting on anything really? But by 'spotting the...

Hi, I have a question regarding vectors. I am thinking ahead regarding an application that I am writing in OpenGL. Currently, four functions make up the vertex calculations, with one independent variable (w2center, w2normal, w2uv, uv2vector). A per-vertex center variable and per-vertex vector...

Homework Statement Given ## d \vec r = dr \hat r + r d \theta \hat {\theta} + r \sin \theta d \phi \hat {\phi}.## Find ## d \hat r , d \hat {\theta} , d \hat {\phi}. ## Homework Equations I know that ## d \hat {e_j} = \omega^i_j \hat {e_i} ## and that ## \omega_{ij}=- \omega_{ji} ## and ## 0 =...

Is the set of all differentiable functions ƒ:ℝ→ℝ such that ƒ'(0)=0 is a vector space over ℝ? I was given the answer yes by someone who is better at math than me and he tried to explain it to me, but I don't understand. I am having difficulty trying to conceptualize this idea of vector spaces...

Homework Statement 3 charges are placed like shown: Q1 __4cm____ Q2 ______6cm___________Q3 Q1=-2nC Q2= 1nC Q3= 3nC Find the resultant force and its direction upon the charge Q3. Homework Equations F=k0*(Q1Q2)/r2 k0-constant, equals to 9*10^9 r-distance The Attempt at a Solution...

I know that If we have a rigid body rotating clokwise direction,the angular velocity vector should be in the into the screen.But also I know that ##w=dθ/dt## so..Whats the equation that tells us that ##\vec w## is into the screen ? Is it coming from some vector product ? Or we know that...

Homework Statement Find unit vector(s) that are parallel to both of the planes 6x + y + z = 1 and x − y − z = 0 . Homework Equations N/A The Attempt at a Solution OK. So here is my reasoning - I find the normal of both the given planes and find the cross product between the vectors. The...

In a vector space can you limit the scalar. For example, if I have Vector space in ℤ2 can i only multiple integer scalars?

I found it very interesting to see that surface charge and the Poynting vector are being used to describe how a simple DC circuit actually works. Chabay and Sherwood have made an outstanding contribution to physics and engineering in their texts and papers. Of course others jump on the...

Homework Statement How do you find the derivative of the radial vector r Homework Equations r [/B]= ru'_r + ru_r r = \frac{dr}{dt}u_r + r\frac{du_r}{dt} can't get latex to work either The Attempt at a Solution [/B] If r is the magnitude of r, how would you find the derivative of it...

Homework Statement As always, I wish I were allowed to upload a drawing ;) This is not a problem, this is a derivation of sorts, so I don't have any numbers. I have 3 points. one at the origin, a point charge q and a test charge Q I have a vector from the origin to the point charge q with a...

I know that the span of any subset of vectors in a vector space is also a vector space (subspace), but is it true that every vector space has a generating set? That is, the moment that we define a vector space, does there necessarily exist a spanning set consisting of its vectors?

I am currently coding a small application that reproduces the transport of a vector along a geodesic on a 2D sphere. Here's a capture of this application : You can see as pink vectors the vectors of curvilinear coordinates and in cyan the transported vector. The transport of vector along...

Homework Statement Determine if the following is a subspace of ##P_3##. All polynomials ##a_0+a_1x+a_2x^2+a_3x^3## for which ##a_0+a_1+a_2+a_3=0## Homework Equations use closure of addition and scalar multiplication The Attempt at a Solution Let ##P=a_0+a_1x+a_2x^2+a_3x^3## and...

Homework Statement Homework Equations The Rotation Matrix The Attempt at a Solution I am sorry but I do not know how to even begin

Homework Statement My problem is: For the logarithmic spiral R(t) = (e^t cost, e^t sint), show that the angle between R(t) and the tangent vector at R(t) is independent of t. Homework Equations N/A The Attempt at a Solution The tangent vector is just the vector that you get when you take the...

Homework Statement Suppose that ##T_i## is the contravariant component of a vector field ##\mathbf{T}## that is constant along the trajectory ##\gamma.## Show that intrinsic derivative is ##0.## Homework Equations $$\frac{\delta T_i}{\delta t} = \frac{dT^i}{dt}+V^j\Gamma^i_{jk}T^k$$ The...

Dear forum, I am trying to understand what a separable vector space is. I know we can perform the tensor product of two or more vector space and obtain a new vector space. Is that vector space separable because it is the product of other vector spaces? thanks

Hello, I try to understand the following demonstration of an author (to proove that dot product is conserved with parallel transport) : ------------------------------------------------------------------------------------------------------------------------ Demonstration : By definition, the...

Homework Statement Darryl drives his load of tomatoes 14.0 km [E], 6.0 km [N], 12.0 km [N 15° E], and then 2.0 km [N 65° E]. This takes him 42 minutes. Calculate Darryl’s distance and displacement. Then draw a diagram to show your work. [/B]Homework Equations Not really sure.[/B]The Attempt...

Homework Statement A golf ball is struck at ground level. The speed of the golf ball as a function of the time is shown in the figure, where t = 0 at the instant the ball is struck. The scaling on the vertical axis is set by va= 16 m/s and vb= 29.3 m/s. (a) How far does the golf ball travel...

I hear the phrase vector mass being used a lot in discussions of various models in particle physics. But I am not exactly sure what it means. There is no Wikipedia article on this term. Is vector mass somehow different from scalar mass? The only possible mass terms in the Lagrangian arise due...

Homework Statement [/B] A plane leaves the airport in Galisteo and flies 180 km at 67.0 degrees east of north; then it changes direction to fly 255 km at 49.0 degrees south of east, after which it makes an immediate emergency landing in a pasture. When the airport sends out a rescue crew, how...

Hey! :o Let $V$ be the real vector space $\mathbb{R}[X]$ and $M \subset \mathbb{R}$ a set with $d$ elements. Let $$U_1 := \{ f \in \mathbb{R}[X] | \forall m \in M : f(m) = 0\}, \ \ U_2 := \{ f \in \mathbb{R}[X] \mid \deg(f) \leq d − 1\}$$ be two vector spaces of $V$. Let $\Phi: V\rightarrow...

Im trying to solve the following problem from the book 'Learning with kernels', and would really appreciate a little help. Background information - Let $\{(x_{1},y_{1}),...,(x_{N},y_{N})\}$ be a dataset, L a Loss function and $H(k)$ a reproducing kernel Hilbert space with kernel $k$. The...

Homework Statement Suppose that a particle follows the path r(t) = 2cos(t)i + 2sin(t)j Give an equation (in the form of a formula involving x and y set equal to 0 ) whose whose solutions consist of the path of the particle. Homework Equations None that come to mind The Attempt at a Solution I...

I'm going through a basic introduction to tensors, specifically https://web2.ph.utexas.edu/~jcfeng/notes/Tensors_Poor_Man.pdf and I'm confused by the author when he defines vectors as directional derivatives at the bottom of page 3. He defines a simple example in which ƒ(x^j) = x^1 and then...

I have some problems in calculating the flux of Poynting's vector through a surface. I have that: S=c/4π⋅H^2⋅n (S: Poynting's vector, n: versor of the direction of the propagation of the em wave) H=1/cR A' but: A=(1/cR) d'; A'=(1/cR) d'' ==> H= (1/cR)^2 d''...

So, the Wiki page on the Poynting vector has this image: I remember hearing/reading somewhere that the energy transmission in a circuit like this is actually not traveling through the wire, but that it actually happens through the electromagnetic field, I.e. essentially the Poynting vectors...

Homework Statement As part of a longer problem: "Find necessary and sufficient conditions for the point with positionvector r to lie inside, or on, the tetrahedron formed by the vertices 0, a, b and c." Homework Equations I am not sure... vector addtion? The Attempt at a Solution I don't...

Homework Statement Homework Equations The Attempt at a Solution So I began by subtracting. (205-160)=55 i (495+128)=623 j Both of these vectors are in the positive direction. So if I divide the vector by its magnitude I should get an answer of 1 in the positive direction for both i and...

Why is ##\theta## a scalar whereas ##d\theta## a vector ?

Surface S and 3D space E both satisfy divergence theorem conditions. Function f is scalar with continuous partials. I must prove Double integral of f DS in normal direction = triple integral gradient f times dV Surface S is not defined by a picture nor with an equation. Help me. I don't...