Vectors Definition and 1000 Threads

Hi there! As you might have already guessed, I'm referring primarily to the 'geometrical' difference (is there such geometry in Hilbert space?) between ##n##-dimensional state vectors | \psi \rangle = \left( \begin{matrix} \psi_1 \\ \psi_2 \\ \vdots \\ \psi_n \end{matrix} \right) and their...

Suppose a change of basis from basis ##B## to basis ##C## is represented by the matrix ##S##. That is, ##S## is the transformation matrix from ##B## to ##C##. Now if ##t## is a given linear transformation, ##t:~V\rightarrow V##, with eigenvectors ##\epsilon_i##, say, and ##T## is the...

In A. Zee "QFT in a nutshell" in chapter I.5 Exercise 1.5.1 on page 39 for spin 2 massive propagator. I know I’m missing something very simple (self-taught beginner). I'm trying to derive equation (13) on page 35, which is G_{\mu\nu,\lambda\sigma} = G_{\mu\lambda}G_{\nu\sigma} +...

Are all quantum states represented by normal vectors?

Homework Statement Find the coordinates of the vector of the height of the parallelogram formed by vectors a={1, 2, 1} and b={2, -1, 0} Homework Equations A=|axb|, A=|a|*h The Attempt at a Solution I can find the intensity of the vector h i.e the length of the height, but not its vector. I...

Homework Statement Use the component method to add the vectors vector A and vector B shown in the figure. The length of vector B is 3.25 m and the angle θ = 28.5°. Express the resultant vector A + vector B in unit-vector notation. Homework Equations x = rcos y = rsin The Attempt at...

I've been trying to solve this question all day. If somebody could point me in the right direction I would really appreciate it! (ii) A particle’s motion is described by the following position vector r(t) = 4txˆ + (10t − t)ˆy Determine the polar coordinate unit vectors ˆr and ˆθ for r. [4]...

I have always been under the impression that a vector is not "fixed" in space. Given any vector, we could just move it around and it would still have the same components (in a cartesian coordinate system). What confuses me, however, is how we define the components of a vector in polar...

Hey! :o We want to show that if $\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$ are on the same plane, then there are $A, B, C$ not all $0$ such that $A \vec a+B \vec b+C \vec c=\vec 0$. The solution is the following: If $\overrightarrow{a}, \overrightarrow{b}...

Homework Statement So I have a function that allows me to input two vectors and it will calculate the resultant vector. The code works fine. I need to call on this function and plot the two input vectors and the resultant; it's easier to explain if you look at the code. Homework EquationsThe...

Consider the following definition: (##M## denotes a manifold structure, ##U## are subsets of the manifold and ##\phi## the transition functions) Def: A smooth curve in ##M## is a map ##\gamma: I \rightarrow M,## where ##I \subset \mathbb{R}## is an open interval, such that for any chart...

Question #7. It says: The (constant) acceleration points in the direction of the difference of the velocities (final minus initial). Note how initial vector is subtracted from the final one (head to tail). But in this video, average acceleration (change in velocity) is found by adding velocity...

Why does the magnitude of a ket vector not matter? The motivation appears to be that a state vector only can decribe a particle, or no particle. But why shouldn't the magnitude of ket vectors not be used to represent the density of the particles, the average number of particles? I'm am fairly...

If you were to have clones of genes you wished to use for FISH in the form of a plasmid, cosmid, BAC and YAC, which would be best for gene mapping? I'm unsure as to what the distinction would be between these types particularly for use in FISH. Which is most commonly used and why? Thanks

What is the motivation for defining vectors in terms of equivalence classes of curves? Is it just that the definition is coordinate independent and that the differential operators arising from such a definition satisfy the axioms of a vector space and thus are suitable candidates for forming...

Homework Statement Find the set of points of M such that: AM x BC=AM x AC (Vectors) The Attempt at a Solution [/b] AM x (BM+MC) =AMx(AM+MC) AMxBM+AMxMC=AMxAM +AM x MC Then AMxBM=0 MA X MB=0 I am new to this lesson and this is my first time i solve such a question and i had no idea...

I have a few conceptual questions that I'd like to clear up if possible. The first is about directional derivatives in general. If one has a function f defined in some region and one wishes to know the rate of change of that function (i.e. its derivative) along a particular direction in that...

Mod note: Member warned about posting with no effort. 1. Homework Statement Expand to the general case to explore how the cross product behaves under scalar multiplication k (a x b) = (ka) x b = a x (kb). The Attempt at a Solution would this be the right general case to portray the situation?

Homework Statement Use three specific vectors in 3 space to show that ⃗ a ×(b⃗ ×c⃗ ) ≠ (a⃗ ×b⃗ )×c⃗ solution is in pdf... Homework EquationsThe Attempt at a Solution

Homework Statement That is, use three specific vectors in 3-space to show that...

Homework Statement Verify (https://ucdsb.elearningontario.ca/content/enforced/4850117-BL_1415Sem2__MAT_MCV4UU-948314_1_ELO/MCV4UPU01/MCV4UPU01A06/images/vec-a.gif?_&d2lSessionVal=Y3hirJUTSYjH76OEZwqHIBATE&ou=4850117 +...

Homework Statement Let u, and v be vectors in Rn, and let c be a scalar. c(u+v)=cu+cv The Attempt at a Solution Proof: Let u, v ERn, that is u=(ui)ni=1, and v=(vi)ni=1. Therefore c(ui+vi)ni=1 At this point can I distribute the "c" into the parenthesis? For example: =(cui+cvi)ni=1...

Hey! :o We suppose that a ship, that is at the position $(1, 0)$ of a nautical map (with the North at the positive direction $y$) and it "sees" a rock at the position $(2, 4)$, is directed to North and is traveling $4$ knots in the relation to the water. There is a current of 1 knot that is...

Homework Statement V1 and V2 are different vectors with lengths V1 and V2 respectively. Find |V1 X V2| if V1 and V2 are perpendicular. Homework Equations V1 X V2 = |V1|*|V2|sin(Θ) The Attempt at a Solution Since sin(90) = 1, V1 X V2 = |V1|*|V2|. When I input this answer it says its incorrect...

Hello! :o I found the following in my notes: The plane that is constructed by two non-parallel vectors $\overrightarrow{v}$ and $\overrightarrow{w}$ consists of all the points of the form $a \overrightarrow{v}+b\overrightarrow{w}$, $a, b \in \mathbb{R}$. The plane that is defined by...

## 1. Homework Statement Let P = (1,1,1), Q = (0, 3, 1) and R = (0, 1, 4). Find the area of triangle PQR Homework Equations ## \frac {|PQ × PR|}{2} ## = area (The crossproduct divided by two) The Attempt at a Solution I lost my answer key, so I want to check if my final answer of ## \frac...

when we are talking about a linear transformation the argument of the function is a coordinate vector...is this true? another question...when i see a column vector...these are the coordinates of the vector with respect of a basis...is this true? for example if i see... (({{1},{3}}))^T with...

Homework Statement I'm stuck on this problem, and I don't really know how to approach it. Homework Equations Pretty much just p=mv And the conservation of linear momentum: total initial mv = total final mv The Attempt at a Solution I tried just plugging in the variables into the...

Homework Statement Dear Mentors and PF Helpers, Here's the question: Homework EquationsThe Attempt at a Solution Here's my solutions: Please let me know whether I'm right. Thank you [/B]

I understand that a tangent vector, tangent to some point p on some n-dimensional manifold \mathcal{M} can defined in terms of an equivalence class of curves [\gamma] (where the curves are defined as \gamma: (a,b)\rightarrow U\subset\mathcal{M}, passing through said point, such that \gamma (0)=...

Hi I have just started looking at direct products and came across the following which i don't understand : the direct product of two spin -up vectors = | 1 > which is in a bigger vector space I don't understand how the direct product is | 1 > ? and in this case is it always a bigger vector...

Homework Statement I'm having trouble with understanding four vectors in particle physics. I'm reading this wikipedia page,http://en.wikipedia.org/wiki/Einstein_notation, and its telling me that ## v^\mu= \begin{pmatrix} \mu_0 \\ \mu_1 \\ \mu_2 \\ \mu_3 \end{pmatrix} ## and ## v_\mu=...

Homework Statement Block B has acceleration of 4 m/s2... Relative acceleration of block A w/ respect to B is 4 m/s2. Find magnitude & direction of accel for A? Homework Equations a_A = a_B + a_A/B x_A = x_B + x_A/B y_A = y_B + y_A/B The Attempt at a Solution x & y components: -4cos(20) =...

Homework Statement [/B] Use vectors and the dot product to prove that the midpoint of the hypotenuse of a right triangle is equidistant to all three vertices. Homework Equations [/B] I know the dot product is A⋅B = |A||B|cosΘ ... or ... A1B1 + A2B2 + A3B3 ... + AnBn I know the...

Homework Statement Homework EquationsThe Attempt at a Solution I tried to attempt the question but I am not sure how to start it, at least for part (i). My biggest question, I think, is how does the multiplication of a random complex number to a Fourier-Transformed signal (V(f)) have an...

Homework Statement Suppose a constant force F acts on a particle of mass m initially at rest. (a) Integrate the formula for acceleration \vec{a} = \frac{\vec F}{\gamma m} - \frac{\vec v}{\gamma mc^2}(\vec F \cdot \vec v) where \gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} to show that the speed...

Hello All, I'm taking a university physics course and while dealing with the introduction to vectors I believe I'm having more trouble at drawing diagrams than with the calculations (trigonometry) and therefore not having a clear diagram is causing some confusion. The problem is as follows...

I am trying to follow a proof that given a Kiling vector ##V^{u}##, the quantity ##V_{u}U^{u} ## is conserved along a geodesic. I am given the Killiing Equation: ## \bigtriangledown_{(v}U_{u)}=0 ## [1] Below ## U^{u} ## is tangent vector ## U^{u} = \frac{dx^{u}}{d\lambda} ## The proof...

I have the feeling that it is, but I am not really sure how to start the proof. I know I have to prove both closure axioms; u,v ∈ W, u+v ∈ W and k∈ℝ and u∈W then ku ∈ W. Do I just pick a vector arbitrarily say a vector v = (x,y,z) and go from there?

Hey, let's say that in 2D space we have a 2x2 rotation matrix R. Normally you could multiply this rotation matrix by a 2x1 column matrix / vector X. In that case it would be XR to get the vector rotated in the way described by R. Now what I'm wondering is, what if I had 3 column vectors that I...

Homework Statement Calculate (A×B)⋅C for the three vectors A with magnitude A = 5.00 and angle θA = 25.1∘ measured in the sense from the +x - axis toward the +y - axis, B with B = 4.18 and θB = 62.0∘, and C with magnitude C = 5.82 and in the +z - direction. Vectors A and B are in the xy-plane...

Homework Statement Find the magnitude and direction of the resultant force Fr=F1+F2+F3 by first finding F'=F1+F2 then Fr=F'+F3 known values are in the link Homework Equations Basic vector addition. Law of cosines. Law of sines. The Attempt at a Solution Here's my attempt. I'm not convinced by...

In Nakahara's book, "Geometry, Topology and Physics" he states that it is, by construction, clear from the definition of a vector as a differential operator [itex] X[\itex] acting on some function [itex]f:M\rightarrow\mathbb{R}[\itex] at a point [itex]p\in M[\itex] (where [itex]M[\itex] is an...

Consider a vertical pendulum affected by gravity (See the pdf file i included). Now i can choose two different opposite directions for my unit vectors which give me different equations. \downarrow : m\ddot x = mg-kx \uparrow : m\ddot x = kx-mg Which of course makes perfect sense, changing...

Homework Statement Find a set of parametric equations for the line of intersection of the planes. 6x-3y+z=5 and -x+y+5z=5[/B]Homework Equations The cross product formula The formula for the parametric equations of a line in three dimensional space: x=x1+at, y=y1+bt, z=z1+ct Knowing the fact...

So I was given this on a recent physics problem. http://prntscr.com/5s8u0u I understand vectors completely, I just don't know where to start. Specifically where it mentions maximum angular separation am I confused. Any type of hints/assistance is appreciated.

Hey, I'm new to this , and I understand the derivation of the transition laws for overlapping regions of a manifold for covectors and vectors starting from thinking of them as a differential and a differential operator respectively, but I don't really have a clue where this comes from... Any...

So this is a bit embarassing. But I enrolled in community college. I really can't wrap my head around vectors or friction. What books useful eh? I'm French btw

I have to prove $\vec x \perp \vec z$ and $\vec y \perp \vec z$ imply $\vec x || \vec y$ where $\vec x,\vec y,\vec z \in \mathbb{R}^2$ and $z$ nonzero. I know $x \perp z \Leftrightarrow x_1z_1+x_2z_2=0$ and $y \perp z \Leftrightarrow y_1z_1+y_2z_2=0$. If two vectors are parallel, I can write...

Is $\begin{bmatrix} 4 \\ 3 \\ 0 \end{bmatrix}$ in $R^3$?