Vector Definition and 1000 Threads

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.

In p.244 of Carroll's "Spacetime and Geometry," the Killing horizon ##\Sigma## of a Killing vector ##\chi## is defined by a null hypersurface on which ##\chi## is null. Then it says this ##\chi## is in fact normal to ## \Sigma## since a null surface cannot have two linearly independent null...

I read in several places that if, for example, a point particle exhibits uniform circular motion about the z-axis within an osculating plane not equal to the x,y plane, then the angular velocity still points along the z-axis, even though the angular momentum does not (it precesses about the...

Homework Statement Could someone explain how the property, $$\nabla (\frac{1}{R}) = -\frac{\hat{R}}{R^2}$$ where ##R## is the separation distance ##|\vec{r} - \vec{r'}|##, comes about? What does the expression ##\nabla (\frac{1}{R}) ## even mean? Homework EquationsThe Attempt at a Solution...

Homework Statement Could someone illustrate why $$\int_{V} \nabla \cdot (f\vec{A}) \ dv = \int_{V} f( \nabla \cdot \vec{A} ) \ dv + \int_{V} \vec{A} \cdot (\nabla f ) \ dv = \oint f\vec{A} \cdot \ d\vec{a}$$ ? Homework EquationsThe Attempt at a Solution I understand that the integrand can...

Homework Statement A -12nC charge is located at (x,y) = (1.0cm, 0cm). What are the electric fields at the positions (x,y) = (5.0cm, 0cm), (-5.0cm, 0cm), and (0cm, 5.0cm)? Write each electric field vector in component form. Homework Equations E=k(q/r2) The Attempt at a Solution I was able to...

My question is simply whether you can reduce a vector triple product, or more generally a scalar multiplier of a vector in a cross product? Given: (A x (uB x C) = v, where u and v are known constants. Is it valid to change that to: u(A x (B x C) = v or (A x uB) = v, can you change that to u(A...

Hi I am studying force components on a inclined plane. I understand the concept of breaking vectors into X , Y Components relative to the horizontal plane however what I can't seem to make sense of is how the ratios of a triangle and the main input force being the hypotenuse of the triangle...

1. Homework Statement Hi, I have done part a) by using the expression given for the lie derivative of a vector field and noting that if ##w## is a vector field then so is ##wf## and that was fine. In order to do part b) I need to use the expression given in the question but looking at a...

Homework Statement Use the relation ##\langle \vec e^a, \vec e_b \rangle = \delta^a_b## and the Leibniz rule to give an expression for the derivative of a dual frame vector ##\frac{\partial \vec e_b}{\partial x^a}## in terms of the connexion components. Homework EquationsThe Attempt at a...

Homework Statement https://i.imgur.com/UtLzb34.png Homework Equations the law of cosinus The Attempt at a Solution I have not been available to scan my work, but I'm kinda stuck at the beginning. And our teacher have not show us this kind of physics yet. Thanks.

Hello everyone, my question is: what are the criteria that must be satisfied for the pushforward of a smooth vector field to be a smooth vector field on its own right? Consider a smooth map \phi : M \longrightarrow N between the smooth manifolds M and N. The pushforward associated with this map...

Homework Statement My mentor has run me through the derivation of equation (3) bellow. I am unsure how he went from (1) to (3) by incorporating the log term from eq(2). In eq(3) it seems he just canceled the relevant n terms and then identified 1/n as the derivative of L however if this were...

Homework Statement A student pushes a 0.65kg box Ali g a desk. When he stops pushing the book, it moves 85cm before stoping (slowing down in this period). Coefficient of friction between book and Table is 0.27.Calculate the work done on the book by the friction. Should it be positive or...