Vector Definition and 1000 Threads

According to my understanding, option D is the only possible value of R. I don't understand how options A, B and C are included. Please explain this question. Thanks. (regards)

Hi all, i tried to do this question but got stuck on the last point . Can anyone help me please? The general form of vector potential: I got the answer for A1 vector potential but don't know what assumptions i need to get the expression for the A2. Does anyone know how one can derive it...

Homework Statement Problem- Determine if the set of all function y(t) which have period 2pi forms a vector space under operations of function addition and multiplication of a function by a constant. What I know- So I know this involves sin, cos, sec, and csc. Also I know that a vector space...

I feel like the vector space ##\mathbb{R}^n## differs from other vector spaces, like ##\mathbb{P}##. For example, if we wrote down an element of ##\mathbb{P}##, like ##1+2t^2##, this is an object in its own right, with no reference to any coordinate system or basis. However, when I write down an...

I learned that the Poynting vector was the electromagnetic density of momentum but recently, while reading the Electromagnetic_stress–energy_tensor article at Wikipedia, I thought about the implications of the momentum conservation equation and arrived to an inconsistency, this equation is...

Homework Statement Two parallel very long threads are uniformly charged with linear charge density of 10-8 C/cm . Distance between them is 15 cm. Find electric field vector at a distance of 15 cm from both threads. Homework Equations E*dA=Qenclosed/permittivity of free space The Attempt at a...

Homework Statement What's the vector equation for a plane which contains the point ##(-2,2,1)## and whose vectors ##(1,1,2)## and ##(2,1,-1)## are parallel to it? Homework Equations I think the relevant here is - The plane equation. The Attempt at a Solution [/B] We can go through...

AIUI, every normal matrix has a full eigenvector solution, and there is only 1 *normalized* modal matrix as the solution (let's presume unique eigenvalues so as to avoid the degenerate case of shared eigenvalues), and the columns of the modal matrix, which are the (normalized) eigenvectors, are...

Given an ##N## dimensional binary vector ##\mathbf{v}## whose conversion to decimal is equal to ##j##, is there a way to linearly map the vector ##\mathbf{v}## to an ##{2^N}## dimensional binary vector ##\mathbf{e}## whose ##(j+1)##-th element is equal to ##1## (assuming the index starts...

Homework Statement Take as input from the user an integer N. We don't want the user to enter very large integers, so exit with an error message if N>20. You may assume that N is an integer (and not a real number) and also that it is positive. Make two vectors v1 and v2 using v1.append() and...

Homework Statement Write an alternate vector equation for the following line. Change both the point and the direction vector: w⃗ =(4,−1,3)+t(−2,1,7) Homework EquationsThe Attempt at a Solution Did I write a proper alternate vector equation here? I'm still new to vectors in 3-space any tips or...

Homework Statement The velocity of a plane is 625 km/h northwest. a) Draw a diagram of this vector, including the magnitude and direction. b) Determine the horizontal and vertical components of this vector. Round your answers to the nearest whole number. c) Give the coordinates of the vector...

Homework Statement Given the following diagram, use vector addition to sketch the resultants: a) u→−2v→ b) 3v→−u→ Homework EquationsThe Attempt at a Solution For this question I am fairly certain that it is correct but for some reason I'm doubting myself. I was wondering if I could get some...

Homework Statement Find u→ in Cartesian form if u→ is a vector in the first quadrant, ∣u→∣=8 and the direction of u→ is 75° in standard position. Round each of the coordinates to one decimal place. Homework Equations none The Attempt at a Solution I'm certain this is correct, but some guy at...

Homework Statement Hi, I'm having some doubts about the gradient. In my lecture notes the gradient of a scalar field at a point is defined to point in the direction of maximum rate of change and have a magnitude corresponding to the magnitude of that maximum rate of change of the scalar field...

Could we have two vector spaces each with its own set of basis vectors. but these basis vectors are related according to the following way. A particular set of vectors in the first vector space may exist "all over the place" but when you represent the same information in the second vector space...

Hi, let ##\gamma (\lambda, s)## be a family of geodesics, where ##s## is the parameter and ##\lambda## distinguishes between geodesics. Let furthermore ##Z^\nu = \partial_\lambda \gamma^\nu ## be a vector field and ##\nabla_\alpha Z^\mu := \partial_\alpha Z^\mu + \Gamma^\mu_{\:\: \nu \gamma}...

I am confused about tensor invariance as it applies to velocity and energy. My understanding is a tensor is a mathematical quantity that has the same value for all coordinate systems. I also understand that a vector is a first order tensor and energy is a zero order tensor. Thus, they should...

On pg. 60 of Nolting Theoretical Physics 1 for the definition of a vector multiplied by a scalar the book shows two little up arrows if the scalar is greater than zero and an little up arrow and then a little down arrow if the scalar is less than zero. Then again on pg. 61 for definition 1.139...

Given w = |v|∙ u + |u| ∙ v. If θ = ∠(u ∙ w) and φ = ∠(v ∙ w) then …. a. Φ – θ = 90° b. θ + φ= 90° c. θ = φ d. θ – φ = 90° e. θ – φ = 180° What I have done: \cos\theta=\frac{u\cdot w}{|u||w|} and \cos\phi=\frac{v\cdot w}{|v||w|} Then I substituted them as |v| and |u| to the given equation and...

Homework Statement u and v are two vectors in the same plane. Vector OM = u+2v Vector OP = 6u+v Vector OQ = 5u +2v Vector OR =2(VecOM) +v Given that ZPQM is a parallelogram, express Vector OZ in terms of u and v.Homework EquationsThe Attempt at a Solution First they wanted me to find Vectors...

Does it make sense to say that a set together with a field generates a vector space? I came across this question after starting the thread https://www.physicsforums.com/threads/determine-vector-subspace.941424/ To be more specific, suppose we have a set consisting of two elements ##A = \{x^2, x...

Suppose we have a scalar function θ(x,y,z,t) of space and time where theta is some angle (0≤θ≤2π) that represents the compact coordinate of a 3 dimensional space (x,y,z) filling membrane at the space time point (x,y,z,t) in a compact space dimension w. Suppose that charge density "pushes" on the...

Homework Statement Hi I have attached an image which shows OK and OM which are position vectors such that OK=k and OM =m R is the mid point of OK and S is a point on OM such that (vec) OS = 1/3 OM L is the midpoint of RM, using a vector method, prove RS is parallel to KL. Homework...

Homework Statement Determine the vector subspace generated by ##A = \{x^2 -x, 3 - x^2, 1+x \} \subset P^2(x)## Homework EquationsThe Attempt at a Solution I tried the usual check of vector addition and scalar multiplication to get the conditions that ##x## and ##y## should satisfy, but...

Hello Everyone. I am searching for some clarity on this points. Thanks for your help: Based on Schrodinger wave mechanics formulation of quantum mechanics, the states of a system are represented by wavefunctions (normalizable or not) and operators (the observables) by instructions i.e...

Hello, I think I understand what a vector space is. It is inhabited by objects called vectors that satisfy a certain number of properties. The vectors can be functions whose integral is not infinite, converging sequences, etc. The vector space can be finite dimensional or infinite dimensional...

Homework Statement Write a vector equation for the line that passes through the point P(–1, 0, 3) and is parallel to the y-axis. Homework Equations (x,y)=(x_0,y_0)+t(a,b) The Attempt at a Solution u ⃗=(0,1,0) (x,y,z)=(-1,0,3)+t(0,1,0)

Homework Statement Find the scalar, vector, and parametric equations of a plane that has a normal vector n→=(3,−4,6) and passes through the point P(9, 2, –5). Homework Equations Ax+By+Cz+D=0 (x,y,z)=(x0,y0,z0)+s(a1,a2,a3)+t(b1,b2,b3) x=x0+sa1+tb1 y=y0+sa2+tb2 z=z0+sa3+tb3 The Attempt at a...

and Lorentz Gauge. Manipulating Maxwell equations and introducing ##\vec A## vector and ##Φ## scalar potentials the following equations are obtained: ## \nabla^2 \vec A+k^2 \vec A=-μ\vec J+\nabla(\nabla⋅\vec A+jωεμΦ) ~~~~~~~~~~(1)## ## \nabla^2 Φ+k^2 Φ=- \frac ρ ε -jω(\nabla⋅\vec...

Homework Statement Two balls with mass m and 4m collide at the location x=y=0 and stick. Their initial velocities just before the collision can be represented as v1=(i+j) v and v2=(j-i)v' respectively. Their final velocity vf makes an angle θ with the +x axis. Find v and v' in terms of vf and...

Homework Statement You enter an antique classic car road rally with your 1956 Studebaker Golden Hawk. The rally course consists of the following segments: travel north at 25.0 m/s for 30.0 min, then east at 32.0 m/sfor 40.0 min, and finally northeast at 30.0 m/s for 50.0 min. For the entire...

<Moderator's note: Image substituted by text.> 1. Homework Statement Given the following vector field, $$ \dfrac{2(x-1)\,dy - 2(y+1)\,dx}{(x-1)^2+(y+1)^2} $$ how do I integrate : The integral over the curve x^4 + y^4 = 1 x^4 + y^4 = 11 x^4 + y^4 = 21 x^4 + y^4 = 31 Homework Equations...

Homework Statement I have an exam on vectors and 2 dimensional motion today. I NEED to know if it is possible to solve any GRAPHICAL VECTOR PROBLEM using only INTEGRATION AND MATH WITHOUT ADDING VECTORS TOGETHER GRAPHICALLY. So given any word problem that is supposed to be solved using that...

Why do we not need to consider direction when determining the change in potential energy? Why do we need to consider it in case of force? Or am I interpreting the question correctly?

What is the covariant derivative of the position vector $\vec R$ in a general coordinate system? In which cases it is the same as the partial derivative ?

hi I am studying algebra and i have a question. why is important that something is a vector space?, i mean, what implications have? matrix, complex numbers , functions , n-tuples. What do these have in common, apart from being a vector space? why is so important that a certain set of...

Homework Statement I have to calculate the partial derivative of an arctan function. I have started to calculate it but I wonder if there is any simpler form, because if the simplest solution is this complex then it would make my further calculation pretty painful... Homework Equations $$\beta...

Hello, I am having trouble understanding a proof presented here: http://www.fen.bilkent.edu.tr/~ercelebi/Ax(BxC).pdf This is a proof of the triple product identity, but I don't understand the last step, where they calculate ##\lambda##. Don't you lose all generality when you state ##\vec A##...

On Riemannian manifolds ##\mathcal{M}## the covariant derivative can be used for parallel transport by using the Levi-Civita connection. That is Let ##\gamma(s)## be a smooth curve, and ##l_0 \in T_p\mathcal{M}## the tangent vector at ##\gamma(s_0)=p##. Then we can parallel transport ##l_0##...

Hello, I am learning about Excited states of Helium in my undergrad course. I was wondering if the total spin operator Ŝ is a vector quantity or not. Thanks for your help.

Homework Statement A plane, diving with constant speed at an angle of 53 degrees with the vertical, releases a projectile an altitude of 730m. The projectile hits the ground 5.00s after release. A plane, diving with constant speed at an angle of 53 degrees with the vertical, releases a...

In my EM class, this vector identity for the angular momentum operator (without the ##i##) was stated without proof. Is there anywhere I can look to to actually find a good example/proof on how this works? This is in spherical coordinates, and I can't seem to find this vector identity anywhere...

Homework Statement A child is flying a large kite of mass 6.8 kg on a windy day. At the moment shown the tension from the string on the kite has a magnitude of 17.0 N and makes an angle of = 32.6° from the vertical, and the acceleration of the kite has a magnitude of ak = 7.72 m/s2 and makes...

Hello, For calculating the mean power at a specific cross section of a waveguide, one can calculate the mean value of the temporal function of Poynting Vector, P(t), where P(t) is the ExHy-EyHx. Note that I am not talking about phasors or a sinusoidal state. If I integrate over the waveguide...

Homework Statement So I have these two Matrices: M = \begin{pmatrix} a & -a-b \\ 0 & a \\ \end{pmatrix} and N = \begin{pmatrix} c & 0 \\ d & -c \\ \end{pmatrix} Where a,b,c,d ∈ ℝ Find a base for M, N, M +N and M ∩ N. Homework Equations I know the 8 axioms about the vector spaces. The...

Homework Statement A sailboat sets out from the U.S. side of Lake Erie for a point on the Canadian side, 90.0 km due north. The sailor, however, ends up 50.0 km due east of the starting point. (a) How far, and (b) in what direction must the sailor now sail to reach the original destination...

Homework Statement In order to solve a question, I need to find the minimum and maximum resultant of three vectors, their magnitudes are given to me. Homework Equations Magnitude of vector A = 1 Magnitude of vector B = 3 Magnitude of vector A = 5 The Attempt at a Solution The maximum part was...

Can anyone help? What is the convention for inserting the vector symbol? I have a draft with -(\vec{2.5})^2 which displays correctly in preview ##-(\vec{2.5})^2\\## why is vec troublesome and underlined in red?? Should I ignore! I realize that I'm not using a variable.

Is there some easy way to see that [\vec{p}^2, \vec{p} \times \vec{L}] is equal zero? I use component method and got that.