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. S

    Chemistry Lewis dot, electronic and molecular geometry

    Draw the lewis dot, identify the electronic and molecular geometry and determine the polarity of a) NO2Cl and b) SOCl2 a) N has 6 valence electrons O has 6(2) = 12 valence electrons Cl has 7 valence electrons Total : 25 For the Lewis Structure: (* is for space) O-N-O **| **Cl I...
  2. D

    Representing a dot product with Sums.

    Is it possible to represent the dot product (matrix multiplication) with sums? For example, know the dot product of a polynomial and another one [i.e. 2+5x and 3x+7x2] would be the sums of the products. [i.e. 2(3x) + 5x(7x2)]. Could this be also written as \sum^{n}_{i=1} a1ibi1? I'm asking...
  3. O

    Questions about matrices and vectors:Why does the dot product of

    Questions about matrices and vectors: Why does the dot product of a and b equal |a||b|cos(angle between a and b) are the vectors of a matrix the columns or the rows, or can it be either? I know a 0 determinant of a matrix means the vectors lie on top of each other, and the absolute...
  4. M

    Can anyone describe to me the difference between dot product and cross product?

    I guess one of them is scalor and one of them is vector, but what is the REAL DIFFERENCE between them? gracias
  5. R

    Static Case Study for dot product

    Homework Statement * With an axis system oriented as shown, the position vectors of points A and B are rA = 175i + 0j + 0k m rB = 39i + 70j + 29k m * When the trolley is halfway between points A and B, the forces exerted on the trolley by the cables are F1 =...
  6. R

    Dot product for Vector equation

    Hi, I have a question about dot product for vector. For detail : https://ecourses.ou.edu/cgi-bin/ebook.cgi?doc=&topic=st&chap_sec=02.4&page=theory Is there anyone understand about it and explain to me the basic concept, why : 1. A • B = |A| |B| cosθ, not A • B =A^2 • B^2 - 2AB cosθ...
  7. R

    Finding integral of dot product of F and dl

    Homework Statement 1. For the vector field F = yz ˆx + zx ˆy + xy ˆz (^x means the unit vector of x) find the integral of F • dl from (0, 0, 0) to (1, 2, 3) in Cartesian coordinates in each of the following ways: (a) along a straight line path from (0, 0, 0,) to (1, 2, 3) (b) along...
  8. B

    Cross product vs dot product headache

    Homework Statement Show (A x B) dot (C x D) in terms of dot products only. Homework Equations A x B = ABsin(theta) A dot B = AB cos (theta) The Attempt at a Solution Subbing both those formulas into the top I got [ABsin(AtoB) times CDsin(CtoD) ] cos(between the two resultant...
  9. G

    Need Help Lewis Dot Diagram - NO+ (nitrosyl)

    Please Help Me Figure Out The Lewis Dot Diagram for NO+ (nitrosyl).
  10. C

    Find x dot as function of t

    Homework Statement find velocity x dot, as function of time t, for particle mass m starts x=0, t=0 subject to force where Fo and c are constants. Fx = Fo + ct Homework Equations answer is x dot =Fo/m t + c/2m t^2 The Attempt at a Solution obviously it is just an...
  11. e2m2a

    Invariance of scalar dot product across inertial and non-inertial frames

    I have a question concerning scalar invariance with respect to an accelerating and an inertial reference frame. Here is the problem. Suppose we have a rotating spherical object, which we denote as the rotator, attached to a near-massless wire. The other end of the wire slips loosely over a...
  12. I

    Dot Product and Perpendicularity

    Homework Statement If |A+B|^2=|A|^2+|B|^2, prove that A is perpendicular to B. Homework Equations A^2=|A||A| The Attempt at a Solution All I can think of to do is expand the equation to get (A.B)(A.B)=A.A+B.B. I know that iff a.b=0, the two are perpendicular but I can't figure...
  13. I

    Vectors and Dot Products: Understanding and Applying Vector Methods

    Vectors, dot products help! OK, I know this is probably really annoying but I have a ton of questions. (I would go to the math tutor but they aren't here yet because the semester just started.) 1. Find the angle POQ by vector methods if P=<1,1,0>, O=<0,0,0>, and Q=<1,2,-2>. What I have...
  14. G

    Dot product between grad f and an arbitrary vector

    Given a function f: R^n -> R, a point x in R^n, and an arbitrary vector v in R^n - is the dot product between grad f and v (evaluated at x) the same as df/dv? If yes, it would be great if someone were to demonstrate a proof. If no, what should be the correct interpretation of the dot product?
  15. N

    Dot Product Differentiation question

    If I differentiate two unit vectors, one with respect to the other, would it just be the dot product between the two vectors (namely the cosine of the angle between them)? I don't understand the physical meaning of the result...
  16. DaveC426913

    Medical Black Dot in Vision: What Is It?

    Lately I've noticed a black dot in the vision of my right eye (a few weeks now). I'm used to floaters, this is different - it's black. Other than that, it's much like a floater: it's out of focus and, while it seems to move around, I think that's just my eye movements (I don't see how it could...
  17. C

    The dot product on electric potential

    there are 2 situations that need explanation. first, the general formula for electric potential as you take potential = 0 at infinity as a reference. Second, the general formula for capacitance on a parallel plate. In situation one, the negative sign does NOT DISAPPEAR, and in the second...
  18. Loren Booda

    Why didn't we see through dot coms, SUVs and subprime lending?

    What is next to watch out for in the world of dubious investments? It's usually a deal, "easy money," or consumerism too good to be true that the public flocks to. How can one gain insight to avoid getting caught up in these speculations?
  19. C

    Problem with dot product of vectors

    It began in class with this problem. Find the dot product of 2 vectors: v1 a vector with components <4, 8> v2 a vector of length 1 angle pi/4 So, i have 2 ways of doing it. 1) v1.v2 = v1x.v2x + v1y.v2y 2) v1.v2 = |v1||v2|cos(theta) And they should come out the same but. 1) v1.v2 =...
  20. B

    What is the Difference Between Dot and Cross Products in Vector Calculations?

    dot product and cross product. i (think dot product is like eg (1,2,4).(2,4,5) = 30 and cross product is like eg(1,2,4)x(2,4,5)=2, 8, 20) but I am not sure... and is there an order like in a.bxc do u do bxc and then.a or do u go normal left to right. but if left to right what's the rule in when...
  21. S

    How Is the Angle Between Two Vectors Determined Using Their Dot Product?

    One vector has a length of 23 units and another a length of 12 units. If the scalar product of these two vectors is 113, what is the angle between the two vectors? A dot B = ABcos(theta) 113 = 12*23*cos(theta) 113/276= cos(theta) cos^(-1)113/276 = theta 65.8 degrees or 66 degrees using...
  22. S

    Get a negative dot product is to have an angle larger than 90 degrees.

    True or False: The only way to get a negative dot product is to have an angle larger than 90 degrees. The formula is ABcos(theta) False because from 3pi/2 to 2pi the cos is positive and 3pi/2 and 2pi is larger than 90 degrees. Right? Stephen
  23. C

    Finding the Dot Product of Vector A & B

    Homework Statement Vector A has a magnitude of 5.00 units, and vector B has a magnitude of 9.00 units. The two vectors make an angle of 49° with each other. Find (vector A)(vector B) Homework Equations The Attempt at a Solution (5i+0j)(0i+9j)= (5N)(0m)+(0N)(9m)= square root...
  24. Peeter

    Reconciling Differential Forms Inner Product of Wedge with GA Dot

    My differential forms book (Flanders/Dover) defines an inner product on wedge products for vectors that have a defined inner product, and uses that to define the hodge dual. That wedge inner product definition was a determinant of inner products. I don't actually have that book on me right...
  25. B

    Inner (dot) Product Inequality: Proving Nonnegativity

    Homework Statement For x,y \in R^n, their inner ("dot") product is given by <x,y>=\sum_{i=1}^n x_i y_i. Also, we write <x,x>=\|x\|^2. Homework Equations Fix p>1. Show that for all x,y \in R^n we have < \|x\|^{p-2}x -\|y\|^{p-2}y, x-y> \geq 0The Attempt at a Solution Expanding the...
  26. K

    Calculating Energy Difference of Quantum Dot in Spherical Well

    Homework Statement A “quantum dot” is a semiconductor device that may be modeled as an electron with an effective mass m that is confined in an infinite spherical well. Suppose that the spherical well has radius a and the electron has effective mass m = f m_e, where f is some real number and...
  27. F

    Calculate del.r(A.r) with Constant Vector A & Distance Vector r

    ı need to learn how can ı calculate ' del . r (A . r) ' where 'A' is a constant vector , 'r' is a distance vector and '.' is dot product. the result must be 4(a.r)
  28. M

    Applications of Dot Product: Finding Force Components on an Inclined Plane

    Homework Statement 15) In Question 14, if the ramp makes an angle of 20 degrees with the level ground. Find the magnitude of the force tending to lift the crate vertically. Textbook Answer for Question 15: 108.3 N ---- 14) A crate is being dragged up a ramp by a 125 N force applies at an...
  29. E

    Multivariable Calculus - Dot Products

    Anyone familiar with dot products of two vectors? What does the dot product show, in other words what is the point of doing a dot product?
  30. T

    Cross product and dot product scalars

    Homework Statement If d1 = 4i - 10j + 2k and d2 = 9i - 10j + 6k, then what is (d1 + d2) · (d1 × 4d2)? Homework Equations Know how to do the cross product and dot product The Attempt at a Solution For the answer i got 9.6i + 56j -127.68k. How do i express that as a scalar for an...
  31. B

    Derivative of the cross and dot product

    Homework Statement If you have two functions dependent on t, A(t) and B(t). Prove their derivatives are as follows: d(A (dot) B) / dt = [A (dot) (dB)/(d(t)] + [d(A)/d(t) (dot) B] {Where "(dot)" acts as the dot product} d(A x B) / dt = [A x (dB)/(d(t)] + [d(A)/d(t) x B]...
  32. rocomath

    Dot Product, what's wrong with my method?

    Find the three angles of the triangle with given vectors. A(1,0) B(3,6) C(-1,4) I found that AB & BC are congruent, so this ends up being an Isosceles triangle and the only angle I need to find is B. BC=<3+1,6-4>=<4,2> AB=<3-1,6-0>=<2,6> \angle B=\cos^{-1}{\frac{20}{\sqrt{20 \cdot 40}}=45^o...
  33. ZapperZ

    U.S. DOT Bans Transport of Spare Lithium Batteries in Checked Baggage

    This is something you might want to take a look before you go off on your next air travel in the US. http://www.powerpage.org/2007/12/us_dot_bans_transport_of_spare_lithium_batteries_in_checked_baggage.html This is going to be a bit annoying since we travel with spare camera and camcorder...
  34. T

    Finding the Position Vector of a Point to Achieve Half Torque of a Particle

    Homework Statement A particle is located at the vector position =(5.00i + 7.00j) m and a force exerted on it is given by =(3.00i + 2.00j) N. (a) What is the torque acting on the particle about the origin? (b) Consider another point about which the torque caused by this force on this...
  35. E

    Geometrical interpretation of dot product?

    Does anyone know what the geometrical interpretation of a dot product in 3-D is? I am calculating the dot product between two vectors in 3d and need to use the |a||b|cos(theta) interpretation basically, but that is for 2d. Can I just tack on an additional cos(theta2)? Thanks a lot for your...
  36. B

    What is the dot product of (b - proj of b onto a) with a?

    Homework Statement I get confused with this problems show that the vector (orth of b onto a) = (b - proj of b onto a) is orthogonal to a. Homework Equations The Attempt at a Solution (b-proj of b onto a) dot a = 0 and I got stuck!
  37. J

    Understanding Vector Dot Product and Gaussian vs. Gauss-Jordan Elimination

    Oh guys, I'm asking for explanations here, a little lesson. If something could explain vector dot product (including it's algebraic method) that would be great. And another thing, what is the difference between Gaussian and Gauss-Jordan elimination?
  38. D

    Help with dot products - How can the dot product be a vector quantity?

    \overrightarrow r (t) is a vector valued function given by: \overrightarrow r (t) = x(t)\overrightarrow i + y(t)\overrightarrow j if h(t) = \left| {\overrightarrow r (t)} \right|, show that the following is true: \overrightarrow r (t) \bullet \overrightarrow r '(t) =...
  39. K

    Solving Dot & Cross Product Equations: Vector Positioning

    Q:Given non-zero vectors u and v, find a vector x such that both equalitites x dot u=|u|, and x cross u = v hold. What should be the mutual position of the given vectors u and v in space, so that the problem has a solution? What I've got so far: Setting x = au + b(u cross v) I have that...
  40. O

    Clarification on a dot product

    This technically a homework question, but needed for homework and understanding for homework to come. Just hope to get it cleared up, thanks again! 1. This formula is given: r_{1}s_{1} + r_{2}s_{s}+ r_{e}s^{3} = \sumr_{n}s_{n} (with the limits etc. not too important). Then, in respect...
  41. R

    Find Projections of b onto a Vector

    ii think i did this correct ( i hate projections) Homework Statement find the scalar and vector projections of b onto a Homework Equations a= (-1, -2 2) b=( 3,3,4) scalr (a dot b)\|a| vector (a dot b)\|a| * a/|a| The Attempt at a Solution (a dot b)\|a| =(1 =6...
  42. M

    How Is the Equation a Dot Product in Momentum Problems?

    Homework Statement Ok so i ran into trouble in the momentum section because i do not understand dot products as well as i thought. I tried going back and revising my notes but nothing new comes to mind. Your help is highly appreciated. ok so let me just state that m1=m2 the problem...
  43. K

    Infinite dimensional vectorial (dot) product)

    If for a function space , we can define the scalar product of any given 2 functions as \int_{a}^{b}dx f^{*}(x)g(x) what happens with its analogue the 'dot/cross' (vectorial product of 2 vectors which is itself another vector orthogonal to the 2 given ones) the question is not in vane...
  44. L

    Dot product and the law of cosines

    I can't seem to derive the law of cosines from the vector addition of C = A + B using the dot product. Does anybody have any insights?
  45. L

    Help with derivation - involves cross & dot products

    Hello, I'm reading a classical mechanics book. In it, they show a derivation of the centrifugal force equation: \vec{ F_{\textrm{cf}}} = -m \vec{ \omega } \times \left( \vec{ \omega } \times \vec{ r } \right) I understood the derivation up to that point. However, they have a couple additional...
  46. S

    What is the meaning of Dot Product

    I just reviewed Dot Product, but I don't know what it actually, exactly means. would you tell me about its physical meaning or something interesting quality of it? Thanks
  47. T

    Calculating Electric Potential: That Tricky Dot Product

    I have become exceedingly confused by the various sign changes involved in computing the electric potential produced by a charge distribution, and I am sure I am simply forgetting a negative sign somewhere and am going crazy. However, V = -int from infty to r of E . ds ds is the...
  48. K

    Is the Dot Product Distributive Property Just Too Simple?

    Need help with this problem. I need to show that one side equals the other. I this is distributive property but isn't that just too plain simple? I mean I am in pre-cal class and therefore this question can't be easy as it seems... ::biggrin: anyways, if anyone knows about vector plez help...
  49. C

    Isopropyl Alcohol Electron Dot Diagram

    Homework Statement Draw out the electron dot diagram for isopropyl alcohol. Homework Equations C3H7OH The Attempt at a Solution Carbon = 4 valence electrons, multiplied by 3 carbons gives us 12 valence electrons for carbon. Hydrogen = 1 valence electrons, multiplied by 8 hyrdogens = 8...
  50. N

    What is the unit vector perpendicular to (2,1,-3) and (-1, 7, 4)?

    Use two methods to determine a unit vector perpendicular to both (2,1,-3) and (-1, 7, 4) Using Cross Product: Let v be a perpendicular vector to the given vectors v = a*b = (2,1,-3)(-1,7,4) =((1)(4)-(7)(-3), (-3)(-1)-(4)(2), (2)(7)-(-1)(1)) =(4+21, 3-8, 14+1) =(25, -5, 15) = (5, -1...
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