Dot Definition and 564 Threads

Use the UPC scheme to determine the check digit for the number $07312400508$. here is the example from the book ok so going with dot product with 07312400508 \begin{align*}\displaystyle &\quad (0731 2 4 0 0 5 0 8)\cdot(3,1,3,1,3,1,3,1,3)\\ &= 0\cdot3+7\cdot1 +3\cdot3+1\cdot1...

Homework Statement I am asked to write an expression for the length of a vector V in terms of its dot product in an arbitrary system in Euclidean space. Homework EquationsThe Attempt at a Solution The dot product of a vector a with itself can be given by I a I2. Does that expression only apply...

Let's take two orthogonal curves in polar coordinates of the form ##\langle r,\theta \rangle##, say ##\langle r,0\rangle## and ##\langle r,\pi/2\rangle##. Cleary both lines are orthogonal, but the dot product is not zero. This must be since I do not have these vectors in the form ##\langle...

Homework Statement a magnetic moment of U = 1 (i) + 2 (k) , surrounded by a magnetic uniform field of B= 3 (i) + 4 (j) - 1 (k) find the potential energy in mJ ? Homework Equations dot product of 2 vectors ( ui*bi)+(uj*bj)+(uk*bk) = or finding the module of both vector and doing AB...

Stumbled on a potential pitfall that can arise if you combine Newton's overdot notation (for time-derivatives) with boldface/non-boldface notation for vectors/vector-magnitudes. Say you have ##\textbf{v}## for velocity and ##\dot{\textbf{v}}## for acceleration. Speed is then ##v## (magnitude of...

Hi. If I have a vector v , say for velocity for example then v.v = v2 and I differentiate wrt t v.v I get 2v.dv/dt but if I differentiate v2 I get 2v dv/dt but v.dv.dt is not the same as v dv/dt so what am I doing wrong ? Thanks

Homework Statement Is the following conclusion correct? Assume there's an equation with vectors on both sides. Taking the dot product of this equation with vectors on both sides loses information, but information will not lose when taking dot products with higher rank tensors on both sides...

I am trying to piece together how the parabolic mirror manages to reflect the "red dot" from the focal point to the eye without distortion. I compare this with a conventional car headlight, which operates almost exactly the same way, except it has a non-transparent backing. Why does the ret dot...

Which is more correct, teaching the first two valence electrons as paired in the electron dot structure or teaching them as not pairing until forced.

So, while textbook was deriving Liouville eq, this is one of step the book uses. I don't understand this step at all. Why is this step true?

Hello I am new here, so it's nice to meet you. I study quantum dot lasers and there is something I don't understand about the energy band diagram. Quantum dots are formed with the Stranski- Krastanov method. For example small InGaAs islands of quantum dots are created on a substrate of InGaAs...

I am planning on making an experiment about intersecting continuous wave laser from 2 or more source on 1 point in thin air. The laser i am planning to use is the simple laser diode, pumped with continuous wave, instead of using pulsed wave as in the usual laser pointer as i don't need it to...

Homework Statement Homework Equations KVL and KCL The Attempt at a Solution I am very confused by the dot convention and how it works when writing your loop equations... I can't find any good videos or explanations online and I am completely lost with this dot convention. So I understand...

∑ab is needed but is impractical to implement. Specifically ∑i ai.10i-|i| in any form where I can work with ∑i ai = α and ∑i 10i-|i| separately. Is there a homomorphic function I can run it through such that ∑ab can be expressed as ∑a∑b? Note: for current problem i cannot simply set it up...

Apparently there's something called the pale blue dot project that needs funding to image an Earth like planet in a nearby star system. I asked them of the lens diameter and they replied that the telescope will use a 18" mirror. Is that enough resolution wise? Seems a little small when you...

I started learning quantum, and I got a bit confused about inner and dot products. I've attached 2 screenshots; 1 from Wikipedia and 1 from an MIT pdf I found online. Wikipedia says that a.Dot(b) when they're complex would be the sum of aibi where b is the complex conjugate. The PDF from MIT...

Homework Statement show that points P, Q and R are in a straight line P (1, -3, 4) Q ( 2, 2, 1) R (3, 7, -2) and find the vectors ## \vec{PQ} ## and ## \vec{QR} ## Homework EquationsThe Attempt at a SolutionIn proving that the points are in a straight line, we might be able to use dot product...

Hey, I want to ask you about the array led component: 1.9mm(0.8’’)8*8 blue dot matrix led displays (model no:KWM-20882XBA). << Edit by Mentor to add link to datasheet >> https://cdn-shop.adafruit.com/datasheets/956datasheet.pdf I saw the technical data sheet but I couldn’t find the...

Hi all, Suppose we have vectors coming in order as A, B and then C (but A must be deleted before C comes in). Then how to get the dot product between A and C? It is allowed to store some calculations of A before deleting elements of A, for example, we could store norm of A, dot(A, B) and etc...

Homework Statement Im given vectors: b = x hat + y hat c = x hat + z hat Homework Equations http://imgur.com/a/iHTOT The Attempt at a Solution so I have 2 eq's... one says: r * s = rscos(theta) the other is a summation saying multiply x component 1 with x component 2, add y component 1...

Why is the dot product equivalent to the matrix multiplication of its components? I've seen some proofs using Pythagorean and cosine law but they don't give you an intuitive feel as to why matrix multiplication works. The geometric definition (##ab cosθ##) is very easy to understand. To a...

Today, my teacher asked us what is the real life utility of the dot product and cross product of vectors. Many of us said that one gives a scalar product, and one gives a vector product. But he said that, that was not the real life utility of the dot and cross product. He asked us, "Students...

Hi everyone, I am currently working on a subject that involves a lot of 4th order tensors computations including double dot product and inverse of fourth order tensors. First the definitions so that we are on the same page. What I call the double dot product is : $$ (A:B)_{ijkl} =...

Hi, hopefully a quick question here...how do you calculate the angle between two vectors if the only information you have is the value of their scalar product and the magnitude of their cross product? Thanks! Andy

When visible light is being emanated to a quantum dot, why is it that you can see specific colors? I am not talking about the fluorescence that would occur when UV light is emanated.

Why does the quantum dot's band gap increase as in shrinks in size? What is the principle behind this? Is the Heisenberg's uncertainty principle?

Hi, I have a long differential equation which I am typing into mathcad. I want to use either dot or dashed notation instead of d/dt to shortern it and make it more readable. Do you know how I can do this so that it actually recognises it as a derivative? I

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...

Hello, I have 2 questions regarding similar issues : 1*) Why does one say that parallel transport preserves the value of dot product (scalar product) between the transported vector and the tangent vector ? Is it due to the fact that angle between the tangent vector and transported vector is...

I was trying to solve a problem involving work , as we know : w = \int_{a}^{b} \vec{f}.d\vec{s} but in my problem the path was cyrcular , so how to evaluate this kind of integral ?

I have seen many instances of molecular formulas of two or more compounds with a dot between two adjacent molecular formulas like CuSO4.10H20, CaCO3.MgCO3, K2SO4.Al2(SO4)3.24H20 and so on. What does the dot indicate?

What is the maximum size of a Quantum Dot? What are the limits of the size of the quantum dots? At what size do we stop calling a Quantum Dot a Quantum Dot?

Okay so I understand that in order to represent a vector which is in cartesian coordinates in spherical coordinates.. we use the transformation which is obtained by dotting the unit vectors. So my question goes like this: when we dot for example the unit vector ar^ with x^ we obtain sin(theta)...

Often I see people using an effective mass model to describe electrons in the bottom of the conduction band. Spin orbit is then included as a perturbation in this effective mass model. But what is the justification for using this sort of model? Would the correct way not be to start from the full...

Homework Statement How would I find the X coordinate of point A. So far I have: A: ( X=? Y=-231.125" Z=175") B: (X=0" Y=0" Z=144") https://physicsforums-bernhardtmediall.netdna-ssl.com/data/attachments/90/90134-44f7db5f8e2c5989352d374160952d17.jpg Homework Equations...

I had a book on dot and cross products, and the author presented his material in terms of Maxwell's equations. It's a popular book. Alas, I can't remember the title or author. I was going to loan it to a friend but found the book missing. The book isn't long at all and is a paperback book...

Problem: Fix some vector ##\vec{a} \in R^n \setminus \vec{0}## and define ##f( \vec{x} ) = \vec{a} \cdot \vec{x}##. Give an expression for the maximum of ##f(\vec{x})## subject to ##||\vec{x}||_2 = 1##. My work: Seems like a lagrange multiplier problem. I have ##\mathcal{L}(\vec{x},\lambda)...

Hi guys, I am looking for a formula which I am sure exits but I cannot locate it. The problem is that a quantum dot absorbs a photon of wavelength λ0(dot is semiconductor or could be any other material). Assuming that it reemits a photon, what is the probability that this emitted photon will...

I am trying to make a connection between the two in terms of the electron configuration for an atom relative to the octet rule for Lewis Dot diagrams. Maybe I just don't understand what the electron configuration represents. Why is it that Lewis Dot diagrams utilize 8 valence electrons as a full...

I am trying to derive the k dot p formula with the spin orbit interaction term included. I am having some trouble. I insert a bloch wave function multiplied with an unspecified spinor. But how do I treat the cross product term that comes from the SO and what is the effect of the pauli matrix...

I have seen a proof for the formula of A.B = ||A|| ||B|| cos(theta)[ proof using the diagram and cosine rule]. In the proof they have assumed that distributive property of dot product is right. diagram is given below c.c =(a-b).(a-b) = a^2 +b^2 -2(a.b) [ here they used distributive law] I...

Why A .A =||A||^2(dot product) in vector analysis. Every where in vector analysis mathematicians used this result. To prove A.B = ||A|| ||B||cos(theta) we assume that A.A is ||A||^2 , without assuming this we can't prove A.B = ||A|| ||B||cos(theta) . I think they assumed it because dot product...

Mission objective: Send a spacecraft to the Alpha Centauri star system and collect data People behind the mission: Mark Zuckerberg, Stephen Hawking, Martin Rees, Pete Worden, Avi Loeb, Freeman Dyson, Lou Friedman, Saul Perlmutter, Philip Lubin, Santa Barabara. Estimated mission launch: 2030s...

Homework Statement This problem actually has 2 parts. For vectors a= (2,p,8) and b= (q,4,12), determine the values of p and q so that the vectors are a)perpendicular b) collinear textbook answer: a) p= 1 and q= -50 (answers may vary) b) p= 8/3 and q=3 Homework Equations a*b = 0 a*b =...

This is I think a really dumb question, but I never got it, why do we have that dot symbol when we integrate. Like in gauss's law, we have ∫E⋅dA . why is that ⋅ there? Thank you for your help

Homework Statement Using index notation only (no expanding of terms), show: \begin{equation*} \text{(a) }\underline{ \bf{a}} \cdot \underline{\bf{A}} \underline{\bf{b}} = \underline{\bf{A}} \cdot \underline{\bf{a}} \otimes \underline{\bf{b}} \end{equation*} Homework Equations...

Homework Statement A point P moves so that its distances from A(a, 0), A'(-a, 0), B(b, 0) B'(-b, 0) are related by the equation AP.PA'=BP.PB'. Show that the locus of P is a hyperbola and find the equations of its asymptotes. Homework EquationsThe Attempt at a Solution AP.PA' =...

Please could someone explain why Earth looks to bright when it is so far away? Also, why can't we see any other objects (other planets and stars) in the image? Thank you.

Homework Statement Use the complex susceptibility to prove that the dot product of E and J is related to the absorption term (the imaginary part - χ'') and independent of the real part (χ'). It is also stated that in order to do is, assume monochromatic field and take the absorption time...

Homework Statement Find the gradient of \underline{\nabla}(\underline{a}\cdot\underline{r})^n where a is a constant vector, using suffix notation and chain rule. Homework Equations On the previous problem,s I found that grad(a.r)=a and grad(r)=\underline{\hat{r}} The Attempt at a Solution...