What is Vector: Definition and 1000 Discussions

Homework Statement Homework Equations above The Attempt at a Solution I'm totally stuck as to how to get to started , how to use the hint to decompose a vector given a preferred spacetime direction. All I know is that any tensor can be decomposed into a anti symmetric and a symmetric...

I need to solve: \dot{\mathbf{r}}=-kv\hat{r} - \dot{\mathbf{r}_s} However, I do not know how to deal with the fact that there is a unit vector. How can this be done? \dot{\mathbf{r}_s} is a constant vector.

Hello, I'm currently doing vectors in class, but I don't know what these parts mean. Especially φ(a,b). I understand cos(φ), but I don't understand cos(φ(a,b)). φ is the angle between two vectors a and b, but what does the (a,b) part add? I tried to google, but I couldn't really find...

My answer was [ (1,2), (0,-1) ] I just wanted to make sure with you guys that you could essentially have an infinite amount of answers. For example: [ (1,2), (0,1) ] [ (1,2), (0, -5) ] etc would all suffice, right?

Homework Statement I have been given a changing magnetic field in cylindrical coordinates. The equation is: \begin{equation} B(r,\phi,z) = - \frac {B_1} {2} r \hat{r} + (B_0 + B_1z)\hat{z} \end{equation} I need to be able to find the magnetic field as a function of x, y, and z. Homework...

I'm reading a textbook on electromagnetism. It says that for two vector fields ##\textbf{F}(\textbf{r})## and ##\textbf{G}(\textbf{r})## their inner product is defined as ##(\textbf{F},\textbf{G}) = \int \textbf{F}^{*}\cdot \textbf{G} \thinspace d^3\textbf{r}## And that if ##\textbf{F}## is...

I am trying to find the most efficient way to select points on a 2d plane from a set that maximizes the area of the of the shape they define when joined together. The points are all paired (sharing the same A->B vector), with these pairs also appearing mirrored about the origin. Here is an...

I need some guidance regarding the directional derivative ... Two books I am reading introduce the directional derivative somewhat differently ... these books are as follows: Theodore Shifrin: Multivariable Mathematics and Susan Jane Colley: Vector Calculus (Second Edition)Colley...

Homework Statement Find the vector form of the equation of the line in ℝ2 that passes through P=(2, -1) and is parallel to the line with general equation 2x-3y=1. Homework Equations None. The Attempt at a Solution vector form: x=p+td general form: ax+by=c --------------------------------...

I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 8: Differentiable Maps and am specifically focused on Section 8.2 Differentials ... I need help in fully understanding Browder's comments on Definition 8.9 ... ... Definition...

I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 8: Differentiable Maps and am specifically focused on Section 8.2 Differentials ... I need help in proving Proposition 8.12 ... ... Proposition 8.12 and the definitions...

I am trying to reconcile apparent differences between the definitions of the derivative of a vector-valued function f: U \rightarrow \mathbb{R}^n (where U \subset \mathbb{R}^m ) of a vector variable from two textbooks ... The textbooks are as follows: Andrew Browder: "Mathematical Analysis...

In this example (https://imgur.com/a/pTFIt) could i define F_1,2 in terms of r-hat_2,1 instead of r-hat_1,2?

Homework Statement Homework Equations The Attempt at a Solution does Vpa has the same direction as Vp? i thought Vp is tangent to the circular path that point P creates( perpendicular to vector Rpa) but from the figure, Vp doesn't seem to be tangent to the path, but Vpa does...

So the Laplacian of a scalar is divergence of the gradient of a scalar field, and it comes out to the double derivative of the field in X, Y, and Z. My book says the Laplacian of a vector field is the double derivative of the X component of the field with respect to X, the double derivative of...

Homework Statement A lightly damped oscillator (mass, m, and spring constant,s, damping constant, b, with one end fixed) under external harmonic force (F0cosωt).(i.e., Standard mass-spring system with lubricated damper, and driven by an external harmonic force.) Since it is lightly...

This is probably fairly simple, but I have a hard time to grasp the concept of the vector potential A in electromgnetism. Especially, in the following equation for the electric field : \vec{E} = - \nabla V - \frac{\partial \vec{A}}{\partial t} When does the second term is not 0 ?

Homework Statement The position vector of an object of mass 0.10 kg at time t in seconds is given by =(^3+5)−4+2^2 Find the velocity and the acceleration as a function of t Homework Equations =(^3+5)−4+2^2 The Attempt at a Solution For velocity I think the equation needs to be...

Homework Statement A physics student studying gravity on the surface of Mars, throws a ball into the air at time t=0s. The ball follows a parabolic trajectory as shown and reaches a maximum height height at t=2s. At t=1s the velocity of the ball is v(t=1s)= 2.00 m/s i + 3.72 m/s j where i and j...

Homework Statement i know how to find the basis of a subspace of R2 or R3 but I can't figure out how to find the basis of a subspace of something like R2,2. I even have an example in my book which i managed to follow nearly till the end but not quite... Given matrix: A= 6 -9 4 -4 show that...

Homework Statement [/B] F =< 2x, e^y + z cos y,sin y > (a) Find the work done by the force in moving a particle from P(1, 0, 1) to Q(1, 2, −3) along a straight path. (b) Find the work done by the force in moving a particle from P(1, 0, 1) to Q(1, 2, −3) along the curved path given by C : r(t)...

Homework Statement Find the unit vectors along which the given functions below increase and decrease most rapidly at P0 . Then find the derivatives of the functions in these directions. Homework Equations solution: The Attempt at a Solution why are the derivatives’ values along these...

I have a sample problem : Photon, with energy E, is absorbed by m. Then, mass m becomes m' (i think it's relativistic mass). Calculate the new mass. My teacher solved the problem as follows; P1=( E/c, P3dphoton); // momentum of the photon P2=(mc, 0); // momentum of the stationary mass...

Homework Statement (a) Consider the line integral I = The integral of Fdr along the curve C i) Suppose that the length of the path C is L. What is the value of I if the vector field F is normal to C at every point of C? ii) What is the value of I if the vector field F is is a unit vector...

Homework Statement Suppose we have a Electic field, E (vector) = kr2r(vector). Find the total charge contained in the sphere of radius R centered in the origin. solution- here E can also be written as kr3r∧, where r∧ is the unit vector this is the given question , so obiously the best way to...

Homework Statement Find th distance of point P to the plane OQR, O being the origin. "PS" is perpendicular to plane "OQR" P(3,-2,-1) S(x,y,z) O(0,0,0) Q(1,3,4) R(2,1,-2) Homework Equations A) The equation in terms of (x,y,z) obtain by triple product of OS,OQ & OR. OS.(OQXOR)=0... [all being...

\begin{align*}\displaystyle \vec{V_2} &=\int_0^3 \left[\left( \frac{4}{\sqrt{1+t}}\right){I}-\left(7t^2 \right){j} +\left(\frac{14t}{\left(1+t^2 \right)^2}\right){k}\right] dt \\ &=\left[\int_0^3 \frac{4}{\sqrt{1+t}} dt \right] {I} -\left[\int_0^3 7t^2 dt\right] {j} +\left[...

Is this the correct partial derivative of B? ##\vec{B} = \frac{g \vec{r}}{4 \pi r^3}## ##\frac{\partial \vec B}{\partial r}## = ##-3\frac{g \vec{r}}{4 \pi r^4} + \frac{g}{4 \pi r^3 }(\frac{\partial r_r \hat r}{\partial r})##

1. Problem: Consider vector field A##\left( \vec r \right) = \frac {\vec n} {(r^2+a^2)}## representing the electric field of a point charge, however, regularized by adding a in the denominator. Here ##\vec n = \frac {\vec r} r##. Calculate the divergence of this vector field. Show that in the...

Homework Statement Which of the following correctly describes the velocity vector in each case? 2. The attempt at a solution I got it wrong at first. My new attempt (I have a sneaking suspicion that I am missing something important): For the first picture: dtheta_1/dt<0 - the angle is...

Hello all, I have a theoretical question regarding subspaces. If V is a subset of a vector space, and we wish to show that V is a vector space itself, we need to show 3 things. Some references say we need to show: a) V is not empty b) V is closed under + c) V is closed under scalar...

Greetings, can somebody show me how to calculate such a term? P= X E² where X is a third order tensor and E and P are 3 dimensional vectors. Since the result is supposed to be a vector, the square over E is not meant to be the scalar product. But the tensor product of E with itself yields a...

I am looks at problems that use the line integrals ##\frac{i}{{2\pi }}\oint_C A ## over a closed loop to evaluate the Chern number ##\frac{i}{{2\pi }}\int_T F ## of a U(1) bundle on a torus . I am looking at two literatures, in the first one the torus is divided like this then the Chern number...

Mod note: Moved to Precalc section Homework Statement Find the midpoint of the vector AB[/B] A(3,2,5) B(1,3,2) Homework Equations Not sure The Attempt at a Solution I wrote each point in terms of the unit vectors, i,j,k then I subtracted the two, and divided by a 2.

$\textsf{write an equation for}$ $\textsf{ The plane through the point (3, 2, -5) and perpendicular to the x-axis}$ 4ok I know this goes thru $3$ on the axis and it is \parallel to the $yz$ plane so is it just $x=3$.

Homework Statement Part b and e. Homework Equations Flux = surface integral of B (dot) ds The Attempt at a Solution I just want to make sure that I have a good understanding of ds. ds is just the direction of the vector that is normal to our area that we are finding our flux throuhg...

Hi, In a demostration i found a change in order i can't understand. how can the differential pass in the beginning part? the only thing I'm sure is that "v" and "dr" are parallel

Hii, As we know, Scaler triple product is volume of parallelopiped constructed by its three sides. Similary, What is the physical significance and geometrical interpretation of Vector triple product ? Also, What are the application where we use such mathematics and why ? Regards, Rahul

Question: A car is moving north at 100km/h. An hour later it is moving east at 100km/h. Its average acceleration during this hour is: a) A vector pointing northeast b) A vector pointing southeast c) A vector pointing southwest d) A vector pointing east e) Zero Attempt: I confidently chose a) A...

Why is it difficult to find really challenging vector analysis problems (problems about Green's, Stokes' and Gauss' theorems in a Calculus 3 course) in Calculus books? Most of the problems are elementary, at least that's the impression I have(I could be wrong). Is it really difficult to...

How do I define a vector starting on the x-Axis at -d/2 ending at d/2 on the x-Axis?

I'm learning Differential Geometry on my own for my research in ML/AI. I'm reading the book "Gauge fields, knots and gravity" by Baez and Muniain. An exercise asks to show that "if \phi:M\to N we can push forward a vector field v on M to obtain a vector field (\phi_*v)_q = \phi_*(v_p) whenever...

$\textsf{Write a complete solution.}\\$ $\textit{ok Let A be the point (1,2,3) and O the origin (0, 0, 0). }\\$ $\textit{Consider the points P (x, y, z) such that AP · OP − OA · OP = 2 − |OA|2.}\\$ $\textit{Show that the set of all such points is a sphere, and find its center and radius.}\\$...

I want to know if i did this problem correctly! Problem: A projectile is traveling with velocity vector v = (30.00 m/s)i + (20.0 m/s)j when it experiences an acceleration of vector a = (-10.00 m/s^2)j. What is its velocity after 2.0 s? What is its speed after 2.0 s? My work: Vy = V0y - gt =...

Homework Statement A pole BC is supported by the cable AB as is shown in the figure. If the magnitude of the force applied on the point B is 70 lb, and the moment of this force about the x-axis is -763 lb ft, determine the pole lenght. I'LL ATTACH AN IMAGE SO YOU CAN SEE IT. Homework Equations...

$\textsf{Find the vector perpendicular to the plane PQR determined by the points}$ \begin{align*}\displaystyle &P(2,1,3), \, Q(1,1,2), \, R(2,2,1)\\ \end{align*} $$\textbf{ solution:}$$ \begin{align*}\displaystyle \vec{PQ}&=(1-2)i+(1-1)J+(2-3)k=&-i-k\\...

Who can make the most impressive, interesting, or pretty TikZ picture? This third challenge is to create a vector diagram. Such as used in geometric figures, or in physical diagrams with forces and velocities, or in state diagrams. For more impressive arrows, we might use the arrows tikz...

Or is it something separate that acts on a geometric space? So we know that the Euclidean space is a vector space. But is it geometric? I ask this because in group theory, the group elements are the operators acting on another set, but clearly we see that this doesn't mean that the group...

Homework Statement I attempted to solve the problem. I would like to know if my work/thought process or even answer is correct, and if not, what I can do to fix it. I am given: Calculate the divergence of the vector field : A=0.2R^(3)∅ sin^2(θ) (R hat+θ hat+ ∅ hat)Homework Equations [/B] The...

Homework Statement A stone is thrown at 25m/s and at 37 degrees above the horizontal from a 20m high building. Take g=10m/s2 Let D be the displacement vector from launch point on top of the building to landing point on the ground, and v be the velocity vector on impact, what is the angle...