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. A

    Dot Product of a Vector with its Derivative

    Hi Guys, I am doing an Electromagnetism course at uni and we just derived Poynting's Theorem in class. However, he left steps for us to fill in and that is why I have a question. In the derivation we get the dot product: B dot dB/dt and E dot dE/dt where both B and E are...
  2. T

    Difference between Inner Product and Dot Product

    Could someone explain me the difference between the inner product and the dot product? Thanks all
  3. P

    Prove c Bisects Angle Between a & b | Dot Product Proof

    Homework Statement If c = |a|b + |b|a, where a, b, and c are all nonzero vectors, show that c bisects the angle between a and b. Homework Equations cos\theta = (a.b)/(|a||b|) The Attempt at a Solution no idea. i struggle with proofs :( please help!
  4. T

    Proving Geometric Fact: u+v Perpendicular to u-v Using Dot Product

    "If u and v are any two vectors of the same length, use the dot product to show that u + v is perpendicular to u − v. What fact from geometry is does this represent." This is basically the last question in an assignment on vectors (first year university, linear algebra). The questions all focus...
  5. H

    Integration of the dot product of two vectors

    Hi, I am having problems understanding the difference between the equations in the files attached profile2.png. where W_i is just representing the ith component of the variable W, and n and v under bars are two vectors, and gamma is a boundary and gamma_e shows is a boundary. what...
  6. B

    Mathematica Mathematica Loop with Dot Product

    Basically, I'm trying to get the various entries of TT to be dotted with the various entries of KK. Each row of TT is a vector while in KK the elements are vectors. So I'm working with different dimensions, but should be able to "call" them still using the right command. My attempt is below...
  7. Kawakaze

    Solving Vectors: Find Dot & Cross Prods of OX,YX & OY,YX

    Homework Statement I already made a start to this question, the position vectors below are worked out in the first part of it, I am 99% sure they are correct so, on to the bit I am stuck on. :) A player stands with his feet at the point O and serves the ball from a point Y at a height of...
  8. P

    Does the Dot Product of Two Non-Zero Vectors Bisect the Angle Between Them?

    Homework Statement if c = |a|b + |b|a where a b and c are all non zero vectors, show that c bisects the angle between a and b, that is, divides it in half. Homework Equations none? The Attempt at a Solution dont know where to start manipulating?
  9. P

    Lorentz Force Question - Where did the y dot come from ?

    Basically the question is about a penning ion trap. You need to use the equation for the Lorentz Force, which I have. It says the trap electrodes have a potential: V(x,y,z) = A(2z^2 - x^2 - y^2); There's a superimposed uniform B-Field B = B(z hat) It then asks you to write down an...
  10. S

    Dot product within the commutator

    So I am reading a book on ferromagnetism, the author writes \left[S_J,S_{J-1} \cdot S_J\right] = S_J cross S_{J-1} (I couldn't get the cross product x in latex code for some reason) Where [tex]S_J[\tex] and [tex]S_{J-1}[\tex] are the spin operators for atoms j and j-1. I was...
  11. C

    Cylindrical and Cartesian Coord. dot product

    Homework Statement I'm given 2 unit vectors a_x and a_theta. I need to find the dot product between the two. Homework Equations Conversion from Cylindrical to Cartesian x = r * sin(theta) y = r * cos(theta) z = z Conversion from Cartesian to Cylindrical r = sqrt(x^2 +...
  12. D

    Integral with dot product in it

    Homework Statement I need to evaluate this integral: \int (\hat{r}\cdot\vec{a})\hat{r}d\Omega where \hat{r} is the radial unit vector, \vec{a} is a constant vector and d\Omega is solid angle element (\sin\theta d\theta d\phi). I saw something similar, but it was with tensors, and...
  13. P

    Dot product / vector magnitudes

    Homework Statement ||V|| = 2 ||W|| = 3 angle between vectors = 120 degrees V(dot)W = -3 Find ||2V+W|| Homework Equations Cos120 = V(dot)W / ||V|| ||W|| V(dot)V = ||V|| ^2 W(dot)W = ||W|| ^2 The Attempt at a Solution instead of solving for ||2V+W|| i instead try...
  14. B

    How Does the Dot Product Interact with the Gradient in Vector Calculus?

    dot product, and the gradient urgent pls!... Homework Statement Δ<-- this be the gradient and B<-- be a vector B X= xi +yj + zk *<---- be the dot product. (B*Δ)X=B Homework Equations n/a The Attempt at a Solution im not sure how to go about this but this is what i did i...
  15. P

    Taking the derivative of a dot product

    Homework Statement Hi, I need to take the derivative of the following energy potential (attached) in order to get an expression of the force so I can do a conjugate gradient minimization. An explanation of the potential is found in the attached jpeg below the functional form. Homework...
  16. L

    Find theta from the cross product and dot product of two vectors

    Homework Statement If the cross product of vector v cross vector w = 3i + j + 4k, and the dot product of vector v dot vector w = 4, and theta is the angle between vector v and vector w, find tan(theta) and theta. Homework Equations vector c = |v||w| sin(theta) where vector c is the...
  17. planethunter

    The Pale Blue Dot: Reflecting on Our Place in the Universe

    I had not seen this photograph in a while, but I recently ran across the “pale blue dot” picture from Voyager. I read Sagan’s deeper description of it and it literally almost brought me to tears as to the true meaning of our existence on this “pale blue dot”. We are so insignificant compared to...
  18. A

    Perpendicular vector using dot not cross product.

    Homework Statement I have 2 (3d)vectors A and B and I want to find a vector C perpendicular to both of them. A = 3i-2j+4k B = -2i+5j-2k C = Cx+Cy+Cz Homework Equations So we know A dot C = 3Cx-2Cy+4Cz and B dot C = -2Cx+5Cy-2Cz The Attempt at a Solution
  19. G

    What Does q*a Dot Product Mean?

    If someone says that you have to take the dot product of q*a and a is a length, and q is the 111 direction, or alonfg the 111 direction. What does that mean. Is it simply 111 dot length a. We have a exponential function to the power q dot a and want to know what to do.
  20. M

    Dot products and angle between cables

    Homework Statement This is actually for an engineering class, but it's pretty basic vector addition. Determine the angle θ between the two cables attached to the post. I've attached the picture. Homework Equations The Attempt at a Solution From the picture: F1: α=? β=...
  21. M

    Dot product - two points and a projection

    Homework Statement A person starts at coordinates (-2, 3) and arrived at coordinates (0, 6). If he began walking in the direction of the vector v=3i+2j and changes direction only once, when he turns at a right angle, what are the coordinates of the point where he makes the turn. Homework...
  22. R

    Application of the Dot Product (Arfken and Weber)

    Homework Statement A pipe comes diagonally down the south wall of a building, making an angle for 45 degrees with the horizontal. Coming into a corner, the pipe turns and continues diagonally down a west facing wall, still making an angle of 45 degrees with the horizontal. What is the angle...
  23. P

    What Does the Dot Mean in a Function Like f(x,·,·)?

    When you see something like f(x,·,·), how are you supposed to interpret it? Sorry, I can't give example, the only places I've seen have been using it informally. I read, http://www.reddit.com/r/math/comments/995dl/ask_math_reddit_what_does_the_dot_in_this/ , but can't find a definitive answer.
  24. B

    Integration by parts of a dot product scalar integrand

    Homework Statement Is this true or false? \int_V {\vec \nabla \Phi \bullet {\bf{E'}} \cdot {d^3}x} = \vec \nabla \Phi \bullet {\bf{E'}} - \int_V {\Phi \cdot \vec \nabla \bullet {\bf{E'}} \cdot {d^3}x}
  25. Q

    Dot product between cross products

    Homework Statement show (axb) . (cxd) = |a.c b.c| |a.d b.d| The Attempt at a Solution i have no idea. i don't know if the lines at the side are modulus lines or matrix brackets but it seems that it has something to do with distribution law. but i can't start proving if i...
  26. L

    Dot Product Question: Find Angle in Basketball Gym

    Homework Statement A basketball gymnasium is 25 meters high, 80 meters wide, and 200 meters long. For a half time stunt , the cheerleaders want to run two strings, one from each of the two corners above one basket to the diagonally opposite corners of the gym floor. What is the cosine of the...
  27. A

    The Pale Blue Dot (a question)

    So as you might or might not know the Pale Blue Dot is a picture taken from the spacecraft Voyager 1 when it was 6.1 billion kilometers away from Earth. To quote Carl Sagan: (of course there is a lot more quotable and more important material, but it serves for the question) "Because of the...
  28. S

    Determining the polarity of mutually inducted voltages using the dot convention

    Homework Statement Determine the polarity of the induced voltages in L1 and L2. [PLAIN]http://img406.imageshack.us/img406/730/31761140.jpg According to the dot convention rule, when current enters the dotted terminal of a coil,the polarity of the voltage it induces in the other coil is...
  29. C

    Vector Cross and Dot Products: Understanding and Solving Problems

    Hey guys, I'm a kinda noobie to this site so I have not much experience with the formatting and stuff here, but anyway was doing some physics and came stuck =P Would really appreciate any help Homework Statement Vectors A and B are drawn from a common point, with the angle in between them...
  30. L

    Question about cross and dot product

    Homework Statement There are two points p1 pointing up p2 pointing rightHomework Equations The Attempt at a Solution I need to find \stackrel{\rightarrow}{p1} * r^ \stackrel{\rightarrow}{p2} X p1^ \stackrel{\rightarrow}{p2}* r^ they got \stackrel{->}{p1} * r^ =0 why is that? i know...
  31. N

    Dot product, cross product, Newton's laws.

    My final for Physics is coming up and I really, really ****ed up in this class. I don't even know how to do dot products, cross products, or let alone Newton's laws. We applied Newton's laws to some pulley problems I think. I've been going to all the lectures but it just doesn't stick -- nothing...
  32. E

    Matrix - Inner Products and Dot Products

    Homework Statement Consider a matrix A in R^(nxn) . In R^n for vectors x and y, define the product <x, y> = ((Ax)^t)(Ay). a) For which choices of A is this an inner product? b) For which choices of A is <x, y> = x (dot) y (the dot product)? Homework Equations For inner...
  33. N

    Why Do We Minimize the Squared Length in Surface Distance Calculations?

    A little clarification is required for the following techniqueTHE TECHNIQUE Given a surface z = f(x,y), and some point Q in R3 (not on the surface) The point P on the surface for which the distance from P(x, y, f(x,y)) to Q is the shortest distance from the surface to Q (i.e. vector PQ has...
  34. R

    How Can You Calculate the Magnitude of Vector A Using Dot Product Rules?

    Homework Statement i'm having troubles solving this problem in physics involving dot product rule Vector B is 5m and 60 degress above the x axis A has the same magnitude as C and C is has 25 more degrees than A .. find magnitude of A.. B dot C = 35 B dot A = 30 this all we're...
  35. C

    Proving perpendicular vectors using Dot Product

    Homework Statement Homework Equations dot product a.b = lal.lblcostheta vectors are perpendicular when a.b = 0 The Attempt at a Solution OA . LA = 0 OA = OM + MA LA = LO + OA OA . LA = (OM+MA) . (LO + OA) = OM.LO + OM.OA + MA.LO + MA.OAi get stuck here
  36. H

    Eigenvectors and the dot product

    Homework Statement Suppose the the matrix A is symmetric, meaning that A = a b b d Show that for any symmetric matrix A there are always real eigenvalues. Also, show that the eigenvectors corresponding to two di erent eigenvalues are always orthogonal; that is, if V1 and V2 are the...
  37. W

    Linear Algebra / Dot Product / matrices

    Homework Statement Let V=Rⁿ and let AεMnxn(R) Prove that <x,Ay> = <A^T x, y> for all x,yεV Homework Equations The Attempt at a Solution Can someone tell me if I'm on the right track? <x,Ay> = x^T Ay = (x^TA)y = <A^T x,Y>
  38. C

    Writing Assembly LC2 Program to Calculate Dot Products of Two Arrays

    how to write an assembly program to calculate the dot products of two arrays ?? Thx Anyone know how to write an assembly program (source code) to calculate the dot products of two arrays with LC 2 ? Given: The size of each array is 15 (a[0],...,a[14] ; b[0],...,b[14]) that are stored in...
  39. FeDeX_LaTeX

    Integration Involving Dot Product?

    Hello; How do I solve an integral involving the dot product? For example, imagine I have two vectors A and B, and I want to calculate; \int \vec{A}\cdot\vec{B} How do I do this? I am asking because, I read somewhere that I have to evaluate the dot product first: \int...
  40. S

    Visualizing the Dot Product Inequality of a, b & c in R^d

    Suppose I have three vectors a,b and c in R^d , And, I have that a.b < c.b(assume Euclidean inner product). What are the ways to visualize relation between a,b and c geometrically? I realize this is slightly open-ended, but am looking for insight here. Thanks in advance. PS: I have a thought...
  41. W

    Weird Dot Product Homework Q: Unusual Answer?

    Homework Statement i have the vector m(x(t), y(t)) = r = (s^t cos(t), e^t sin(t)) and want to find the line integral of itHomework Equations 1. \int m \centerdot r' dt 2. \int |m| |r'| dtThe Attempt at a Solution the answer is sqrt(2)/2 (e^pi - 1). when i do the problem the first way, i do not...
  42. P

    Understanding Dot Products & Summation Convention

    definition \{\vec{A},\vec{B}\}\cdot \vec{C}=\vec{A}(\vec{B}\cdot\vec{C}) \vec{C}\cdot \{\vec{A},\vec{B}\}=(\vec{C}\cdot\vec{A})\vec{B} I have a question. I found in some books that definition of tensor is \hat{T}=\{\vec{T}_k,\vec{e}_k\} where \hat{\T} is tensor! Is here...
  43. I

    Linear algebra involving dot product and orthongal matrices

    Homework Statement Given: x (dot) y = x^T * y (where x,y are vectors; dot is dot product; and x^T is x transpose) and R is an orthogonal nxn matrix, and x,y are elements of R^n Show ||Rx|| = ||x|| The Attempt at a Solution I'm not sure what information I am suppose to use to solve...
  44. H

    What do dot and cross product mean in electromagnetics?

    Hello. I am taking a fundamentals of electromagnetics. There are couple of formulas I have been using without understanding the concepts. \nabla \cdot B = 0 \nabla X E = 0 (curl free) In those cases, what do dot and cross product mean? Thanks.
  45. M

    Vectors dot product and cross product help

    Homework Statement Vectors A and B (both with the lines over it) lie in an xy plane. Vector A has magnitude 8 and angle 130 degrees, Vector B has components Bx=-7.72 and By=-9.2. a)What is 5(vector A) dot vector B? b)What is 4(Vector A) cross 3(vector B) in unit vector notation and magnitude...
  46. D

    Proving the Dot Product and Norm Theorems

    Homework Statement The Attempt at a Solution I let D be the center x = DX & a = DA (x-a) * (x+a)=|x|^2-|a|^2 Dunno what to do with the right side of the equation
  47. S

    Simple dot product [inner product] (verification)

    Homework Statement Homework Equations know dot product The Attempt at a Solution PART A PART B not sure what's it asking for help would be great
  48. O

    Can the Dot Product of Two Unit Vectors Ever Be Less Than 1?

    I need certain stopping criterion for approximating one unit vector with another. In case there is a perfect match (after a number of iterations), the dot product of the vectors is 1. I need to know (and have a reasoning for) whether in any other case the dot product of the original unit vector...
  49. B

    Properties of cross and dot products

    Homework Statement let u be a nonzero vector in space and let v and w be any two vectors in space. if u.v = u.w and u x v = u x w, can you conclude that v=w? give reason for your answer. Homework Equations The Attempt at a Solution v is not necessary equal to w since u is nonzero...
  50. B

    Dot Product Question, Perpendicular

    pretty much this is all i was given. I have no idea how to even approach it. I do not need an answer (would be nice though), just an idea on how to go about starting it.
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