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. I

    Proof of Dot and Cross Product of Arbitrary Vectors with Pauli Spin Operator

    I need to show: (\mathbf{\sigma} \cdot \mathbf{a})(\mathbf{\sigma} \cdot \mathbf{b})=\mathbf{a} \cdot \mathbf{b} I + i \mathbf{\sigma} \cdot (\mathbf{a} \times \mathbf{b}) where a and b are arbitrary vectors, sigma is the pauli spin operator. I was just wondering what the dot product...
  2. R

    Dot product of electric and magnetic field conserved in special relativity?

    An inertial reference frame 2 is moving along the x-axis with constant velocity v with respect to inertial reference frame 1. ......->-> ->-> How can i prove the E.H = E'.H' ?? (dot product) using the 4 dimensional (Ax,Ay,Az,phi) where E = -1/c dA/dt - gradiant(phi) and H = curl(A) Where E is...
  3. L

    Verify Your Lewis Dot Diagrams: Get Expert Feedback and Improve

    Hi, I am not too sure about my lewis dot diagrams, can someone check them and let me know if anything is wrong with them, thanks.
  4. J

    What Are the Basics of Calculating Cross Products in Vector Algebra?

    I was wondering if anyone could give me information the base of cross product all the problems I have been reading about so far have been in real depth I need to understand the basics first the problems given here are the beginning, if anyone can give me any help please do so, and thank you in...
  5. D

    Dot product cross product, where did they come from?

    While taking linear algebra I never really understood where the dot and cross product came from. It seemed that they were just randomly defined. I know that the dot product is an inner product but why is it defined as: \vec v \cdot \vec u = v_1 u_2 + v_2 u_2 ? why not \vec v \cdot \vec u =...
  6. C

    Setting up an optical sensor with a dot sequence

    Homework Statement Needan optical sensor to detect a dot sequence on widgets passing 50cm away from the sensor. Want each dot to exactly cover the sensor. If the dots are 10mm in diameter and the sensor is 40mm in diameter, what is the position and focal length of the lens to do the...
  7. A

    Finding Possible Values for K in Vector Algebra

    Hi I'm new here and I'm having trouble with this algebra question please help. Sorry if my latex is ugly I'm new to it. I get stuck at the bottom line and I'm not sure how to go further with the question to solve for K #7 - Angle between 2 vectors is \alpha where cos\alpha = \frac{3}{7}. a =...
  8. S

    Calculating the DOS for spherical quantum dot

    Dears Is any method to calculate the density of states of spherical (purely) quantum dot?
  9. P

    How to Solve Cross and Dot Product Problems with u, v, and w?

    Ok, this one has really got me... Suppose that u \centerdot (vXw) = 2. Find (a) (uXv) \centerdot w (b) u\centerdot(wXv) (c) v\centerdot(uXw) (d) (uXv)\centerdotv Once I understand the what to do with the information given, I am sure the rest of the problems will fall into place...
  10. L

    Applications of vector dot product in physics

    I have to present shortly five applications of vector dot product in physics, for example: W=F*s. I am not quite clear about vectors, so could someone advise me.
  11. T

    Vectors with appl of dot product

    I'm trying to solve this problem with different approaches. Link is here http://img138.imageshack.us/img138/2268/problem1eb1.th.png the answer is 0i + 0.0927j + 0.0232 k lb* Means DOT Method one: Find the force in scalar components. Then Take the cross product of two position vectors to get...
  12. T

    Work done on a force using dot product

    The question with all the info is: A force F = (6x i + 5y j) N acts on an object as it moves in the x direction from the origin to x = 5.04 m. Find the work (work = integral of F (dot product) dx done on the object by the force. I am confused as to what dx would be in this equation, and how...
  13. J

    Vector question: dot product in cylindrical coordinates

    Hello. To find the work of a force, I have to perform a dot product between the force and a infinitesimal displacement. If they are in cylindrical coordinates, I can't manage to make the dot product. Please, could you help me? Thank you.
  14. T

    How Can Vector C Be Expressed in Terms of A, B, and u?

    Hello, my problem is as follows: Given that A and B are known vectors, and A \cdot C=u is a known quantity, and A \times C=B Express C in terms of A,B, u, and the magnitude of A So far what i have done was use the definition of the dot product as AC cos \theta=u, and cross product as AC...
  15. W

    Dot products - why does the vector become scalar

    As Gokul43281 correctly pointed out to me, the dot product of two vectors is a scalar. I looked up this page to read about this. Thing is, I think conceptually. I could simply accept that this is so, but I don't "see" why it so. As my screen name implies, I must know why something is so...
  16. F

    Dot product of basis vectors in orthogonal coordinate systems

    I'm doing a series of questions right now that is basically dealing with the dot and cross products of the basis vectors for cartesian, cylindrical, and spherical coordinate systems. I am stuck on \hat R \cdot \hat r right now. I'll try to explain my work, and the problem I am running into...
  17. H

    Prove Rectangle: Dot Product Help

    -Use the dot product to prove that the quadrilateral with vertices A(-4,1) B(4,5) C(7,-1) and D(-1,-5) is a rectangle. I tried find AB dot BC = 0, but I'm not getting 0. So I'm stumped. Can someone help me out? =/
  18. G

    Understanding the Derivative of a Dot Product: A Question on the Product Rule

    I have come across something that seems a little strange to me. The derivative of a dot product is something similar to the product rule. I am having difficulties grasping this. Isn't the dot product of two vectors a scalar? And then I always thought of a scalar as a real number and the...
  19. T

    Izit possible fabricate the quantum dot by cvd?

    izit possible if i take nanoporous alumina or nanoporous silicon into the cvd. use the gallium powder n flow the ammonia gas... can it make a gaN quantum dot? any idea to fabricate quantum dot without mbe? i think there sure has a simple and cheap way to make it... any idea? tanx
  20. CarlB

    How Does Clifford Algebra Apply to Quantum Physics?

    I registered the website http://www.CliffordAlgebra.com . My purpose is to have a website that gives a decent education in the practical uses of Clifford Algebra, as I am interested in their applications to physics. Is there any desire over here for a more mathematical introduction to the...
  21. W

    Cross & Dot Products in Physics: A Comprehensive Guide

    Can someone help me understand about the cross product and dot product? And how and where can I apply it in physics in solving problems.
  22. D

    Are Inner Products and Dot Products Fundamentally the Same?

    Is there any difference between an inner product and a dot product?
  23. B

    What Does 'Quantum Dot Exciton' Mean?

    Why do we talk about " quantum dot excitons" ? For me, excitons and quantum dots are two distincts objects For me, excitons (at least in a bulk) are a bound state of an electron and a hole, bound by the attractive coulomb potential, and their binding energy and wavefunctions are the one of a...
  24. H

    Can you help with Electron Dot Structures for these 6 compounds?

    I got another problem with my Chemistry Homework. I need to put the Electron Dot Structure for the following. 1) Lead Oxide 2) Potassium Sulphide 3) Sodium Nitride 4) Silver Oxide 5) Copper Chloride 6) Calcium Chloride Hope somone can help
  25. infraray

    Dot Product Calculator Quandry

    I'm going nuts here and I can't figure this out. I have two complex vectors: A=(1+i)x + (1)y +(i)z B=(4-i)x +(0)y + (2-2i)z If I do the dot product of these on my calculator I get 1 + 7i, however when I do this by hand I keep getting 7 +5i. What am I doing wrong? When figuring this out by...
  26. E

    Rules regarding the vector cross product and dot product

    hi, I'm currently doing a mechanics module at Uni. The thing is, I'm not very sure about rules regarding the vector cross product and dot product. For example, it says in my notes for angular momentum: "Introducing polar coordinates \mathbf{r} = r(cos \Phi \mathbf{i} + sin \Phi...
  27. A

    Name Geometric Shapes Based on Lewis Dot Drawings

    Give each group a shape name based on geometry. This one does not have to be "correct," but I want you to remember what the molecules look like for application later in the unit. H2O NH3 CH4 H2S CCl2F2 I've drawn both a Lewis dot drawing and a stereo projection for each but I still...
  28. L

    How to: Force, work & dot product

    A force in the xy plane is given by: F= - (b/r3) (x i^ + y j^) where b is a positive constant and r= sqrt(x2 + y2) a) Show that the maginitude of the force varies as the inverse of the square of the distance to the origin and that its direction is antiparallel (opposite) to the radius vector...
  29. B

    Differentiation and dot product

    Can someone help me with the following question. I've been having trouble with problems of this kind for a while now. Q. If the path u(t) (u is a vector) is differentiable at least three times, simplify: \frac{d}{{dt}}\left[ {\left( {u' \times u''} \right) \bullet \left( {u' - u}...
  30. M

    Dot product with 3 dimensions, confused on concept, easy question i think

    Hello everyone! I'm confused on what I'm suppose to do here, I think i might got it though but i need to make sure... Here is the problem and my work: http://show.imagehosting.us/show/764032/0/nouser_764/T0_-1_764032.jpg he let r(t) = f(t) i + g(t) j + h(t) k. So if i multiply this by...
  31. K

    How Does the Electron Dot Diagram for CN Look?

    how would the electron dot diargram for CN look? i am tired and stumped.
  32. M

    Dot product, i don't see what they want from me

    hello everyone, i understand the dot product and its properties but i don't get what they want! They say... The dot product of two vectors are perpendicular if a.b = 0. Then any vector in R^3 perpendicular to -5 -6 -3 note: that is a matrix above. can be written in the form...
  33. D

    Geometric Proof of Dot Product: |A dot B| ≤ |A||B|

    I am doing a assingment for my classical mechanics class that requires the proof of: The dot product of |A dot B| <= (less than or equeal to) |A| |B| . I did the algebraic proof fine but we are required to do a geometic proof as well. This leaves me with the question what is the geometic...
  34. U

    Dipole Dipole and Lewis Dot structes

    Why doesn't HOOH dipole dipole forces? I read that if a molecule has an Oxygen atom, it's likely to have dipole forces. This one only has Dispersion forces. Also, why does the Lewis structure of this molecule NOT look like this:
  35. M

    Showing dot product is commutative, please

    Hello everyone. I'm trying to show ab = ba. //communative property of dot product This is what I have, is it enough to show this? ab = (ax, ay, az) \dot (bx, by, bz) = axbx + ayby + azbz; a\dotb = (axi + ayj) (bxi + byj); //note: i and j are unit vectors = axbx(i)(i) + ayby(j)(j) +...
  36. M

    Conceptual explanation of Dot Product

    I'm a peer leader for a general physics lab and someone asked me to explain what the Dot Product meant conceptually. I told him it was the projection of A onto B multiplied by the magnitude of B. He looked even more confused after that; my questions are: a) Did I explain it correctly...
  37. M

    Show the commutative property with dot product

    Hello everyone, does anyone know the proof of the dot products communative property (a)(b) = (b)(a) or any websites that show the dot products communative property? or other properties? Thanks! The book only shows the distributed property.
  38. D

    Understanding Dot Product: Identity and Unit Vectors

    What is the dot product of a unit vector (e) with a non-unit vector (A)? Is this some sort of identity? Thanks, don_anon25
  39. D

    Questions concerning cross products, dot products, and polar coordinates

    Question answered! Thanks!
  40. M

    Integration involving a dot product

    I am trying to do the following vector integral. When the force and the initial motion are along the same line it is easy but when they are not I can't do the integration. Hints would be appreciated. \vec F = \frac {d} {dt} \vec p where \vec F = (0, F_{y},0) and \vec {p} can be...
  41. S

    Learning vectors: the dot product of vectors

    Well, I've been attempting to learn dot products of vectors and in doing so have come upon some questions. NOTE: a, b, and c are to be regarded as vectors Please regard '*' as the dot for multiplication, too. Question 1: a * b * c When I see this, I am unaware how to approach it...
  42. C

    Mystery of Jupiter's Red Dot: Uncovering the Cause

    why does the red dot on Jupiter i think its like a storm or something or a hurricane but does anybody know why it does not stop? and the cause of it ? thak u craig
  43. J

    Simplifying Dot Product Equations with Vectors - Need Help!

    i need help with the following: note that the big dots represents the dot product 1. suppose that a \bullet b = c \bullet b for all vectors \overrightarrow{b} . show that \overrightarrow{a} = \overrightarrow{c} . i suppose i can't simply divide out the b, right? anyway, i tried...
  44. A

    How do you draw electron dot diagrams for pentyne?

    I am having a difficult time understanding how to do dot diagrams, more specific for "pentyne"
  45. P

    Keeping only one digit after the dot.

    Hello, Is there a mathematical way to get rid of all the digits after the dot except one? 10.292288.. how do i just make it 10.2?
  46. M

    What Are Some Dot Product Questions in Geometry and Discrete Class?

    I have some questions from my geometry and discrete class.. #1 Given a and b unit vectors, a) if the angle between them in 60 degrees, calculate (6a+b)●(a-2b) b) if |a+b|= root(3), determine (2a-5b)●(b+3a) #2 The vectors a=3i-4i-k and b=2i +3j-6k are the daignols of a parallelogram...
  47. P

    Can you help me draw multiple Lewis dot structures for ClO4-?

    I'm asked to draw 5 possible lewis dot structures for this ion. But I can only think of one. which I 've attached here. I'm supposed to draw them and determine which is the most favorable. I know I can do that by calculating hte formal charges, but first I need to draw these structures. Any...
  48. A

    Quantum Dot Problem (Griffiths 7.20)

    Hello, Damn Griffiths 3-star problems... The setup for the potential is a 2D cross basically, so there's a column of zero potential 2a wide (straddling the y-axis) going to +/- infinity, and there's the same thing on the x-axis, so they cross over the origin. Everywhere else the...
  49. RadiationX

    Understanding Vector Dot Product: Solving for a, b, and c in a Right Triangle

    i have three vectors: a=4,b=3,c=5 that form a right triangle. vector a is in the positive x direction, vector b is in the positive y direction starting at the tip of a. vector c is the hypotenuse of the triangle with tip at the origin. (see attaced picture .doc file) the questions are...
  50. S

    Understand Lewis Dot Structures: Cl F & Triple Bonds

    What would the Lewis structure look like for Cl F? Would it look like this: http://img53.exs.cx/my.php?loc=img53&image=dot8pn.png How do you know when there is a triple bond? ~Thanks
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