What is Dot: Definition and 562 Discussions

The Red Dot Design Award is a German international design prize awarded by Red Dot GmbH & Co. KG. There are prize categories for product design, brands and communication design, and design concept. Since 1955, designers and producers can apply for the prizes, with the winners being presented in an annual ceremony. Winning products are presented among others in the Red Dot Design Museum on the premises of the historical Zollverein Coal Mine Industrial Complex in Essen. The Red Dot Design Museum Essen, the first Red Dot Design Museum, was built in 1997. The second Red Dot Design Museum was built in Singapore in 2005. The Red Dot Design Award had more than 15,500 submissions from 70 countries in 2014, and in 2016 alone, 1,559 Red Dots were awarded, 102 of them in the "Best of the Best" category.

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  1. C

    I Absolute value bars in dot product derivation

    Dose someone please know why they have the absolute value bars in this derivation? many thanks!
  2. TGV320

    I Law of Cosines in Linear Algebra: Understanding the Dot Product of Unit Vectors

    HI, I am studying linear algebra, and I just can't understand why "Unit vectors u and U at angle θ have u multiplied by U=cosθ Why is it like that? Thanks
  3. O

    I Dot product of two vector operators in unusual coordinates

    Hi. I hope everyone is well. I'm just an old person struggling to make sense of something I've read and I would be very grateful for some assistance. This is one of my first posts and I'm not sure all the LaTeX encoding is working, sorry. Your help pages suggested I add as much detail as...
  4. J

    Understanding the Dot Product and Cross Product in Vector Calculations

    Could anyone explain the reasoning from step 2 to step 3? Specifically, I don't understand how to find the product of a cross product and a vector - like (v1 · v2)v1 and (v1 · v3)v1. I'm also confused by v1 × v3 + (v1 · v3)v1 -- is v1 × v3 = v1v3? How would this be added to (v1 · v3)v1? Thank you.
  5. Addez123

    Exploring the Correct Calculation of Gradient on Dot Product

    Calculating dot product then doing gradient on it gets you: $$(2xz + z^2, 3y^2, x^2 + 2xz)$$ which is the correct answer. Using the formula, which you're required to do, gets a whole different answer. Lets do each term individually. ##(B \cdot \nabla)A## $$(B \cdot \nabla) = 1$$ ## (A \cdot...
  6. D

    Why does the dot product in this solution equal zero?

    Hi everyone I have the solutions for the problem. It makes sense except for one particular step. Why does the dot product of a and b equal zero? I thought this would only be the case if a and b were at right angles to each other. The solutions seem to be a general proof and should work for...
  7. Halc

    I Cat Chasing Red Dot Faster Than c: Results & Analysis

    This topic assumes special relativity only, so no gravity is involved. I wanted to know how a superluminal thing would appear to an observer, and two of the 'things' I thought of were a moiré pattern and the red dot projected by a laser pointer. The former can be discussed, but this post will...
  8. ubergewehr273

    I Capping layer in semiconductor quantum dot fabrication

    Hi everyone, I've been studying about semiconductor heterostructures and in particular quantum dots. I was wondering, why is there a need to have a "capping" layer above the layer where the quantum dots are formed within a sample? Thanks in advance!
  9. H

    I Sum of the dot product of complex vectors

    Summary:: summation of the components of a complex vector Hi, In my textbook I have ##\widetilde{\vec{E_t}} = (\widetilde{\vec{E_i}} \cdot \hat{e_p}) \hat{e_p}## ##\widetilde{\vec{E_t}} = \sum_j( (\widetilde{\vec{E_{ij}}} \cdot {e_{p_j}}*) \hat{e_p}## For ##\hat{e_p} = \hat{x}##...
  10. A

    How do I calculate the work done by a force field using the dot product?

    y = 10*(1 + cos(0.1*x)) --> dy/dx = -sin(0.1x) dW = F*dx + F*dy = 10*sin(0.1*x)dx + 10*sin(0.1*x)*-sin(0.1x) integrating we have -100*cos(0.1*x) -10*sin(0.1x)^2 from 0 to 10*pi = W = 43 J. The answer says 257 J. Where am I wrong here?
  11. A

    I Confused about dot product of a and b = |a||b| if theta = 0

    I am not sure what I am doing wrong but dot product of a and b =/= |a||b| when I am trying to calculate it. Theta = 0: dot product(a and b) = ax*bx + ay*by |a||b|= sqrt((ax^2+ay^2)*(ax^2 + by^2)) = sqrt((ax*bx)^2 + (ax*by)^2 + (ay*bx)^2 + (ay*by)^2) =/= ax*bx + ay*by What am I doing wrong?
  12. M

    Dot product: ##\vec{D} \cdot\vec{E}## in SI units

    I'm trying to calculate the electrostatic energy, and I'm wondering what happens when I dot the D-field and E-field, with Si-units V/m**2. This is my equation: D dot E = (-4x(epsilon) V/m**2)(-4x V/m**2) + (-12y(epsilon) V/m**2)(-12y V/m**2) Are the final Si-unit still V/m**2 or V**2/m**4?
  13. Wrichik Basu

    Changing proxy server for WiFi in Amazon Echo Dot and Fire TV Stick

    One of my relatives has an Amazon Echo Dot and a Fire TV Stick. Both are connected to the same WiFi. Recently, their internet provider changed the proxy settings such that the default proxy no longer works. They have provided a set of proxies that can be used instead. We have manually set those...
  14. U

    Vectors in yz and xz plane dot product, cross product, and angle

    I tried to find the components of the vectors. ##a_y =2.60 sin 63.0 = 2.32## and assuming the z axis would behave the same as an x-axis ##a_z =2.60 cos 63.0 = 1.18## ##b_z =1.30 sin 51.0 = 1.01## making the same assumption ##b_x =1.3 cos 51.0 = 0.82## I now think I should have switched these...
  15. Blackbear38

    Using Inner Product Properties to Solve Vector Problems

    Summary:: I need to solve a problem for an assignment but just couldn't find the right approach. I fail to eliminate b or c to get only the magnitude of a. Let a, b and c be unit vectors such that a⋅b=1/4, b⋅c=1/7 and a⋅c=1/8. Evaluate (write in the exact form): - ||4a|| - 3a.5b - a.(b-c) -...
  16. A

    Quantum dot tattoo vaccine marker

    Hey, I found these interesting articles about a proposed way of vaccinating people while also applying a biomarker on them which would help remember one's vaccination status. https://news.rice.edu/2019/12/18/quantum-dot-tattoos-hold-vaccination-record/...
  17. B

    I Why is (N dot N) different for magnitude than for X, Y, Z components?

    I have to perform a calculation on my data. Here is an example of data from just one time step (data from other time steps would appear as additional rows). X Y Z Total 2 2 1 3 Total = SQRT(X2 + Y2 + Z2). The calculation I have to do is: (N • N), where "N" is an average. I tried...
  18. greg_rack

    Basic vector operations, using cross and dot product

    Hi guys, I am losing my mind over this passage... I cannot understand how to get from the first expression with the cross products to the second ##\dot{\textbf{r}}(\textbf{r}\cdot \textbf{r})-\textbf{r}(\textbf{r}\cdot\dot{\textbf{r}})##
  19. garthenar

    Engineering Cadence Transformer dot convention and polarity (xfmr)

    Here is the circuit... Here is my work so far in cadence (I haven't put in values for other components in because the moment I saw the dot convention I started trying to figure that out). Where I'm at -There apparently isn't a way in Cadence Virtuoso (the program my class uses) to change the...
  20. F

    Python Dot Notation: Access Functions, Classes, Objects & Variables

    Hello (again). I have become quite familiar with the dot notation in Python. The dot "operator", assuming operator is the right term, seem to have many uses. For example: 1) After an instance name, it can be used to access instance attributes and apply instance methods to the object/instance...
  21. JackFyre

    B Dot Products -- Some questions to help my understanding

    Just a little doubt regarding vector dot products- From what I understand(which may be wrong), dot products are the products of the magnitudes of the two vectors. The equation is given as a · b= |a|x|b|cos θ Can this be understood as the magnitude of a x the magnitude of b in the direction of...
  22. Another

    Problem about dot product in probability density problem

    I don't understand why ? ## \Psi ∇ ⋅ (A \Psi^ *) + \Psi ^* ∇ ⋅ (A \Psi ) = 2 ∇ ⋅(A \Psi ^* \Psi) ## form ## ∇ ⋅ (fg) = ∇f ⋅ g + f(∇ ⋅ g) ## Attempt at a Solution ## \Psi ∇ ⋅ (A \Psi^ *) + \Psi ^* ∇ ⋅ (A \Psi ) = 2 ∇ ⋅ (A \Psi ^* \Psi) - ∇\Psi ^* ⋅ A\Psi - ∇\Psi ⋅ (A\Psi ^*) ##
  23. F

    I Dot product in spherical coordinates

    I'm learing about antennas in a course, and we are using Jin's Electromagnetic text. This isn't a homework problem, I'm just trying to understand what I'm supposed to do in this situation. This part of the text discusses how to evaluate a radiation pattern. One of the steps to evaluate the...
  24. H

    Proof of a dot product using sigma notation

    Mentor note: Moved from a technical section, so is missing the homework template. Hi, I'm always not sure how to prove something in math and I'm wondering if this is enough. ##\vec r \cdot (\vec u + \vec v) ## ##\vec u + \vec v = (u_1+v_1, u_2+v_2,u_3+v_3) = \vec s## ##\vec r \cdot (\vec u +...
  25. LCSphysicist

    Solve this vector system containing sum and dot product equations

    Seems to me the answer is a specific vector: The second forms a plane, while the first X is just a vector. The intersection between the λX that generates the (properties of all vectors that lie in the...) plane (i am not saying X is the director vector!) How to write this in vector language?
  26. T

    I Dot product in Euclidean Space

    Hello As you know, the geometric definition of the dot product of two vectors is the product of their norms, and the cosine of the angle between them. (The algebraic one makes it the sum of the product of the components in Cartesian coordinates.) I have often read that this holds for Euclidean...
  27. D

    I Fundamentals of Astrodynamics: Dot Product Question

    I'm reading Fundamentals of Astordynamics by Bate, Mueller, White and having trouble with this passage (pg15): "2. Since in general a⋅a' = a a'..." I don't think that this is the case. For instance in uniform circular motion r⋅r' = 0. Would appreciate if anyone has some insight into this.
  28. P

    Conclusion about wave propagation in SR given L dot S = N = L' dot S'

    The problem I am having is "What can you conclude about wave prorogation in SR given the results?". The best I can come up with is that the number of wave planes N crossing a section of spacetime in either frame is the same. The section may be bigger or smaller depending on which frame you're in...
  29. P

    O and P whose 4-velocity and 4-acceleration have a dot product of 0

    If ##\tilde{U}_0 \cdot \tilde{A} = 0## in one frame then I would imagine it is also zero in another frame because from my understanding is that dot products are invariant under boosts. So let's boost to the rest frame of O. In that frame ##\tilde{U}_{0T} = \left( c, 0,0,0 \right)## and as...
  30. T

    I Differentiating the Dot Product's Evil Twin

    Hello, I found this link very useful: https://www.quora.com/Why-is-cosine-used-in-dot-products-and-sine-used-in-cross-products I understand all of Anders Kaseorg's discussion except for ONE PONT. At the very end, he writes: "[the evil twin of the dot product] is not differentiable at parallel...
  31. T

    I Dot Product with Derivative

    Summary: The Dot Product of a Vector 'a' and a Derivative 'b' is the same like the negative of the Derivative 'a' and the Vector 'b'. Hello, I have the following Problem. The Dot Product of a Vector 'a' and a Derivative 'b' is the same like the negative of the Derivative 'a' and the Vector...
  32. Kirkkh

    B Why is sine not used for dot product?

    There’s a old 2012 post on here “Why sine is used for cross product and cosine for dot product?” —there are a lot of great answers (which is how I came about this forum). After reading over the replies, it occurred to me: really it’s just because cosine is the “start” of a unit circle. Which...
  33. K

    Why doesn't Pac-Man eat the dot? Berkeley's AI course 188

    Hello! I've been following Berkeley's AI course, and I'm a little stuck. In this video , at 1 hour, 11 minutes, and 55 seconds, there's a short simulation of what they claim to be a depth-2 minimax algorithm applied to the Pac-Man scenario with two dots. Pac-Man begins in the corner. The...
  34. S

    MHB Find Dot Product Between Vector CD & Vector K

    Hi! I'm given 2 points C(2;6) and D(0;10), a vector A with its components = (-3, 2). I'm asked to find the dot product between vector CD and an unknown vector K, knowing that K is perpendicular to A, same norm as A and with a negative x-component. I know that perpendicular means the dot...
  35. kennethellen

    Force Free Motion of a Symmetric Top: Direction of phi dot

  36. A

    B Calculating the dot Product of \nabla and Vector Identity

    From the vector identity ##\nabla •fA=f(\nabla • A)+A•\nabla f## where f is a scalar and A is a vector. Now if f is an operator acting on A how does this formula change?? Like ##\nabla •[(v•\nabla)v]## where v is a vector
  37. P

    Intuition behind dot product

    I know that a dot product of 2, 2 dimension vectors a, b = (ax * bx) + (ay * by) but it also is equal to a*bCos(θ) because of "projections". That we are multiplying a vector by the 'scalar' property of the other vector which confuses me because that projection is in the direction of the...
  38. ibkev

    I Dot product definition: deriving component form

    ## \newcommand{\ihat}{\hat{\boldsymbol{\imath}}} \newcommand{\jhat}{\hat{\boldsymbol{\jmath}}} \newcommand{\khat}{\hat{\boldsymbol{k}}} ## Several times now I've seen the following technique for deriving the component form of the dot product. It always felt clean and simple until last night when...
  39. T

    I Strange Dot Product definition

    Hi i have seen in abook the dot product defined as follows: Dot(A,B)=(1/4)[Norm(A+B)^2-Norm(A-B)^2] how this definition connect with the common one: Dot(A,B)=Sum(ai*bi) Thanks!
  40. Christopher Rourk

    A Is the Fenna-Matthews-Olson complex a quantum dot?

    The FMO complex has a size that is within the typical size range for quantum dots, and absorbs photon energy at what appears to be an effective bandgap between 2-3 eV. While various techniques have been used to investigate the behavior of the FMO complex, such as femto photography or...
  41. Christopher Rourk

    A Quantum Dot Solids: Electron Minibands & Potential

    Do electron minibands in quantum dot solids have a potential?
  42. L

    B Line Integral, Dot Product Confusion

    From my interpretation of this problem (image attached), the force applied to the point charge is equal and opposite to the repulsive Coulomb force that that point charge is experiencing due to the presence of the other point charge so that the point charge may be moved at a constant velocity. I...
  43. G

    Dot convention inductors in series: equation confusion

    Homework Statement So I'm really confused with mutual inductors and dot convention. If your answer is going to be a link to any website I can assure you I read them all and that only left me more confused. So here are my questions: Homework Equations 3. The Attempt at a Solution [/B] ->...
  44. E

    The sign of F (dot) dl when finding electric potential

    The electric potential can be defined as V = - ∫C E⋅dl where we are taking the line integral along C from some convenient reference point O, where we have set V = 0, to the point r we are trying to find the potential at. Of course, C can be any curve, but it's usually the most convenient to...
  45. E

    How do transformers work, and how to read dot notation

    <Moderator's note: Moved from a technical forum and thus no template.> Hi all, I have attempted this question but have a few queries on how transformers work, and what the dot notation represents. (a) The flux would be clockwise around the iron core. (b) This is the question where it gets a...
  46. learning_physica

    Work: Dot Product and Integral?

    I’m having trouble understanding the relationship between how work is both a dot product and integral. I know that work equals F • D and also the integral of F(x): the area under the curve of F and D. However, let’s say that I have a force vector <3,4> and a displacement vector of <3,0>. The...
  47. archaic

    B Dot product scalar distributivity

    I'm having a little trouble with this : We have ##(\alpha\vec{a})\cdot b = \alpha(\vec{a}\cdot\vec{b})## but shouldn't it be ##|\alpha|(\vec{a}\cdot\vec{b})## instead since ##||\alpha \vec{a}||=|\alpha|.||\vec{a}||## ? ##(\alpha\vec{a})\cdot b = ||\alpha\vec{a}||.||\vec{b}||.\cos\theta =...
  48. M

    How can I prove that the dot product is distributive?

    Homework Statement Prove that for vectors A,B and C, A.(B+C)=A.B+A.C and prove the property that for two vectors, A and B the dot product is equal to A^ie_i . B^je_j = e_i.e_jA^iB^j Homework Equations Only use the definition where for two vectors a and b the (length of a)(length of b)cost...
  49. karush

    MHB 412.0.10 ok so going with dot product with 07312400508

    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...
  50. M

    Dot product and basis vectors in a Euclidean Space

    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...
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