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. tomdodd4598

    Can the Dot Product of Four Vectors Maintain Positive Component Signs?

    Hi there, I understand that taking the dot product of two four vectors automatically applies the metric tensor to the second vector. Is there a way to take write the dot product, using vector notation, in a way which keeps the signs of all of the components positive? Thanks in advance.
  2. phys-student

    Dot products in spherical or cylindrical coordinates

    Homework Statement I'm doing a question that requires me to take the dot product of 2 vectors in spherical coordinates. Both vectors have only an r component, can I just multiply the r components? Homework EquationsThe Attempt at a Solution
  3. J

    Can I use a dot product of accel. and vel. to find displace.

    Homework Statement at what initial speed would a projectile have to start at when ejected at 35 degrees to the horizontal from a point A to a point B which is 9.4km distance away in the horizontal and 3.3km below it. taking g as 10m/s[/B]Homework Equations I'm not really sure if these equations...
  4. Z

    Simple spherical quantum mechanics question: r dot p

    Homework Statement Maybe I missed it, but in my notes and also in documents like (http://ocw.mit.edu/courses/physics/8-05-quantum-physics-ii-fall-2013/lecture-notes/MIT8_05F13_Chap_09.pdf) (equation 1.64), I see $$ \vec{r}\cdot\vec{p} = -i\hbar r \frac{\partial}{\partial r} $$ Where ##r## is...
  5. R

    Where to put the dot on radicals (notation)

    This may seem a bit pedantic but I'm writing a report and have radicals in it and notice that some papers put the dot in different places, so my question is does it matter where you put the dot? thanks for any advice
  6. Peeter

    Conditions for the X dot P expectation to be constant?

    Homework Statement Under what conditions is \left\langle{{\mathbf{x} \cdot \mathbf{p}}}\right\rangle a constant. A proof of the quantum virial theorem starts with the computation of the commutator of \left[{\mathbf{x} \cdot \mathbf{p}},{H}\right] . Using that one can show for Heisenberg...
  7. A

    3D Statics Equilibrium - Dot Everything with Vector P?

    Homework Statement Bead B has negligible weight and slides without friction on rigid fixed bar AC. An elastic cord BD has spring constant k = 3 N∕mm and 20 mm unstretched length, and bead B has a force of magnitude P in direction BC. If bead B is positioned halfway between points A and C...
  8. C

    MHB Vector dot product in spherical co-ordinate

    Hi, I am interested to see how to use the vector dot product formula in spherical coordinate system, $$ V_1= r + \theta, at (1,0,0)$$ and $$ V_2= r - \theta, at (1, \frac{\pi}{2}, \frac{\pi}{2})$$ how to evaluate their dot product? do I have to transfer them into cartesian system? what would...
  9. R

    Earth's Blue Hues: Exploring the Science

    Why does the Earth appear blue (mostly) when observed from outside. Blue light is more energetic than red and lower wavelength. Processes which happen on Earth seem to suggest that higher energy light arriving should be absorbed in one way or another and eventually some of it radiated away in...
  10. P

    Proving volume of box using cross and dot product

    Homework Statement The diagram shows a box with parallel faces. Two of the faces are trapezoids and four of the faces are rectangles. The vectors A, B, and C lie along the edges as shown, and their magnitudes are the lengths of the edges. Define the necessary additional symbols and prove...
  11. P

    Finding dot product, cross, and angle between 2 vectors

    Homework Statement [/B] Vector A lies in the yz plane 63.0 degrees from the +y axis, has a positive z component, and has a magnitude 3.20 units. Vector B lies in the xz 48.0 degrees from the +x axis, has positive z component, and has magnitude 1.40 units. a) find A dot B b) find A x B c)...
  12. M

    Dot Products With Orthogonal Vectors

    Homework Statement The Vector a= -2i -3j and is orthogonal to vector b that has the same length as a. The third vector c has the dot products ca= 8m^2 and cb= 9m^2. What are the components of c? c = ______i + _____ j m Homework EquationsThe Attempt at a Solution I know that (a⃗ +b⃗ )⋅c⃗ =a⃗...
  13. A

    Who can work with comsol multiphysics software? (spherical quantum dot)

    hi who can help me with my problem in comsol multiphysics? i want to calculate a schrodinger equation for a spherical quantum dot under applied magnetic field, who can help me? anyone here have the program doing this? help me if you can. i don't know if there is another program for compute...
  14. M

    Problem involving dot and cross product

    Homework Statement https://www.dropbox.com/s/8l90hahznjlv9d0/vector%20problem.png?dl=0 Homework Equations Dot and Cross product The Attempt at a Solution although I know the dot and cross product, I'm not sure what I'm being asked or how to proceed? any help?[/B]
  15. W

    Dot product for vectors in spherical coordinates

    Hi all. I'm struggling with taking dot products between vectors in spherical coordinates. I just cannot figure out how to take the dot product between two arbitrary spherical-coordinate vectors ##\bf{v_1}## centered in ##(r_1,\theta_1,\phi_1)## and ##\bf{v_2}## centered in...
  16. K

    Dot product vs trigonometry in Gauss' law

    I'm currently writing my EP on various physical equations including Maxwell's equations, and I had to justify using the dot product of the normal unit vector and the electric field in the integral version. However, I can't think of a reason for not using trigonometry as opposed to the...
  17. S

    Dot product in the Gravitational Potential Energy formula

    This is the gravitational potential energy formula $$U = -\int_\infty^r\vec{F}_\text{field}\cdot d\vec{r}$$ If r vector's direction is form infinity to r, then it means it has same direction as Gravitational Force. So cos0=1 But after multiplication there is a negative sign here: "-GMm" $$U =...
  18. Pronoy Roy

    Why cross product has a direction but dot product doesn't?

    Can anyone tell me why?
  19. Seung Ju Yoo

    Understanding the Dot Product Formula: An Explanation and Example

    In a book I was reading, it says F=mv'=P' so dot producting on both sides with v F ⋅ v = mv ⋅ dv/dt = 1/2 m d(v2)/dt = d(1/2 m v^2)/dtI really don't get how v ⋅ dv/dt = 1/2 d(v2)/dt. I have seen few threads and they say it's about product rule, but they don't really explain in detail. Could...
  20. N

    Double Dot Product: Solving 3D Vector Problem

    Hi, I have following problem of double dot product (\vec a \cdot \vec b)(\vec a^* \cdot \vec c), and I have expected rusult |a|^2(\vec b \cdot \vec c), but I don't know if it is the exactly result (I am unable to find any appropriate identity or proove it), or it is just an approximation...
  21. Mathias

    Vertical motion Velocity and Acceleration dot products

    Homework Statement A ball is tossed straight up into the air so that it moves in the vertical direction without air resistance. Is there a point where the dot product of the velocity with the acceleration is: a. Zero b. Negative c. Positive d. now assume the ball moves in a parabolic path...
  22. C

    Dot product in uniform circular motion question -- Finding angle?

    I've attached an image of part a of the question to this thread. My question is this (the solution to these former homework problems are posted to help us study for exam, which is why know this already): The angle between the two velocity vectors is determined to be pi/2. How? I know that dot...
  23. R

    Euclidean space: dot product and orthonormal basis

    Dear All, Here is one of my doubts I encountered after studying many linear algebra books and texts. The Euclidean space is defined by introducing the so-called "standard" dot (or inner product) product in the form: (\boldsymbol{a},\boldsymbol{b}) = \sum \limits_{i} a_i b_i With that one...
  24. B

    Use vectors and the dot product to prove the midpoint

    Homework Statement [/B] Use vectors and the dot product to prove that the midpoint of the hypotenuse of a right triangle is equidistant to all three vertices. Homework Equations [/B] I know the dot product is A⋅B = |A||B|cosΘ ... or ... A1B1 + A2B2 + A3B3 ... + AnBn I know the...
  25. ognik

    Vector multiply that is NOT dot or cross?

    Hi - just working through my text (studying by correspondence) on Del operator - so Curl, div etc. Came across some identities parts of which which have me confused. what does it mean when a vector is shown as multiplying something - but without dot or cross? For example F(∇.G) or ∇(F.G) or...
  26. E

    Calculating Power of a Solar Panel

    Homework Statement If at some particular place and time the sun light is incident on the surface of the Earth along a direction defined by the unitary vector – vˆ , where vˆ =(4, 3, 5)/sqrt (50) and with a power density P, what is the total power captured by a solar panel of 1.4 m2 and with...
  27. A

    Finding a basis for a particular subspace with Dot Product restrictions

    Find the basis of the subspace of R4 that consists of all vectors perpendicular to both [1, -2, 0, 3] and [0,2,1,3]. My teacher applies dot product: Let [w,x,y,z] be the vectors in the subspace. Then, w-2x+3z=0 and 2x+y+3z=0 So, she solves the system and get the following: Subspace= {...
  28. S

    How can I calculate the speed of the kaon using four-momentum conservation?

    Homework Statement So a kaon moving at some speed in the +x direction spontaneously decays into one pion and one anti-pion. The anti-pion moves away with velocity of 0.8c, and the pion moves away with velocity of 0.9c. Mass of kaon = 498 MeV/c^2 Mass of pion/anti-pion = 140 MeV/c^2...
  29. R

    Drawing a Lewis Dot Structure for Octathiocane (S8)

    Homework Statement How can I draw a Lewis dot structure for octathiocane (S8) which is non-cyclic, net neutral, and which does not violate the octet rule? Homework Equations None. The Attempt at a Solution First, I tried drawing a straight chain molecule, but the two terminal...
  30. J

    Understanding the Inner Product and Dot Product in Linear Algebra

    I'm just trying to understand from a linear algebra standpoint how they define dot product from the inner product and how this gives rise to a definition of length and angle. somehow there is a way to combine points in space to a scalar value that unambiguously determines length and angle? Is...
  31. M

    Confusion with Dot Product in Polar Coordinates with the Metric Tensor

    Alright, so I was reading up on tensors and such with non-Cartesian coordinate systems all day but now I'm a bit tired an confused so you'll have to forgive me if it's a stupid question. So to express the dot product in some coordinate system, it's: g(\vec{A}\,,\vec{B})=A^aB^bg_{ab} And, if...
  32. A

    Can the Dot Product be Customized to Change Linearly?

    So, is there anyway to make the dot product change linearly? What I mean by this is when the angle is 45 degrees, I want it to be 0.5 instead of 0.7071 as you can see in this image: Instead I want 45 degrees to be 0.5, 60 degrees to be 0.33 and 30 degrees to be 0.66. Same would apply for...
  33. A

    Dot product of a vector and a derivative of that vector

    I'm reading through Douglas Gregory's Classical Mechanics, and at the start of chapter 6 he says that m \vec{v} \cdot \frac{d\vec{v}}{dt} = \frac{d}{dt}\left(\frac12 m \vec{v} \cdot \vec{v}\right), but I'm not sure how to get the right hand side from the left hand side. If someone could point...
  34. J

    Double dot product in Cylindrical Polar coordinates

    Hello, I'm working with a problem in linear elasticity, and I have to calculate the strain energy function as follows: 2W = σijεij Where σ and ε are symmetric rank 2 tensors. For cartesian coordinates it is really easy because the metric is just the identity matrix, hence: 2W = σxxεxx +...
  35. A

    Cross and dot product of two vectors in non-orthogonal coordinate

    Hi everyone, I have to find out how to do cross and dot product for two vectors in non-orthogonal coordinate system. thanks
  36. fluidistic

    Can the Operator n dot L Have the Same Eigenvalues as Lz in Quantum Mechanics?

    Homework Statement I've been told that the operator ##\hat n \cdot \hat {\vec L}## has the same eigenvalues as ##L_z##. Later I've been told that it has the same eigenvalues as any component of ##\hat {\vec L}##. But I am a bit confused, as far as I understand the eigenvalues of ##L_x##...
  37. M

    Dot Product of Equilateral Triangle

    Homework Statement In an equilateral triangle with sides u, v, w, where they are all unit vectors, find u dot w. Homework Equations u dot w = |u||w|cosθ The Attempt at a Solution The answer is ##\frac {-1} {2} ## cos(120) = -1/2 Elsewhere, I read the statement that since these are...
  38. R

    The dot or cross product of two operators acting on a state

    If a system is made up by two subsystems, for example, the atom and the photon. and let's assume the state of the atoms is described by |\phi\rangle, while the state of the photons can be described by |n\rangle, The Kronecker product of the |\phi\rangle and |n\rangle can be used to describe the...
  39. 22990atinesh

    Intuitive meaning of Dot Product

    I know intuitively that the Cross Product of two vectors ##\vec{A}## and ##\vec{B}## represents another vector ##\vec{A \times B}## perpendicular to it. In study of physics we come across this situation a lot. Hence I can visualize some applications of it I know that the dot product of...
  40. U

    Lewis Dot Structures: Understanding Mistakes for Chemistry Tests

    So 3 days ago I had a chemistry test and part of the test included Lewis dot structures. I counted my valance electrons and distributed them equally but I have no Idea why I got these wrong.The second one I know why I got wrong but the rest of them look fine to me. I would really appreciate it...
  41. E

    Dot Product of a Unit Vector with the Negative of itself

    Homework Statement I am trying to calculate the flux for the octant of a sphere, and I am trying to figure out how the mathematics, dot products, and dA works in the integral. I already did the quadrant for \hat{θ} where θ= π/2 (the bottom quadrant) and I did the left quadrant where \hat{n}...
  42. O

    Vectors - dot product and cross product?

    Vectors -- dot product and cross product? Hello may i know when to dot product and cross product?? both look to same to me..
  43. E

    Can a dot product be negative in case of length?

    Let's say A and B are 2 vectors with length in cm and the angle between them is 170°. Obviously, the dot product of A and B will give cm2 as unit but since the value of cos(170) is negative, will the dot product be negative (something)cm2?
  44. P

    How Do Dot and Cross Products Differ in Describing Physical Phenomena?

    I am trying to understand the difference from a physical phenomena point of view, not just math. Surprisingly I think I got the cross product like in rotational momentum. You have the momentum vector and we have effective distance from the momentum vector R that needs to be perpendicular to the...
  45. M

    Dot Product of a Vector and its Derivative- Reality

    Hey everyone, This has been bugging me for a bit. I think I'm probably missing something pretty easy. A dot B= ABcos(θ), where θ is the angle between A and B. There is the little shortcut that says where B is the derivative of A, A dot B= AB. Clearly then cos(θ) = 1, and the angle between a...
  46. D

    Lewis dot structure, octet rule for a central atom

    As you can see, octet rule isn't satisfied for the central atom Xe, it has 2 more electrons attached to it. So does it mean, that you should first try to make sure octet rule works for any "side" atoms, and then you just put any remaining electrons to a central atom? (or central atoms?) And if...
  47. Lebombo

    Projection Using Dot Product Finding a Force (Boat Problem)

    "Projection Using Dot Product" "Finding a Force" (Boat Problem) Homework Statement ------------------------------------------------------------------------------------------- A 600 pound boat sits on a ramp inclined at 30 degrees. What force is required to keep the boat from rolling down...
  48. P

    Dot product of vector and del.

    I'm not sure which section is best to post this question in. I was wondering if the expression (u $ ∇) is the same as (∇ $ u). Here $ represents the dot product (I couldn't find this symbol. ∇=del, the vector differentiation operator and u is the velocity vector or any other vector
  49. jdawg

    How do I solve the dot and cross product of 3i and jxk?

    Homework Statement The value of 3i(dot)(jxk) Homework Equations The Attempt at a Solution I know the answer is 3, but could someone please explain how to work this problem?
  50. S

    MHB These two problems are based on Vectors, dot product and distance for sphere.

    Problem 1: Let S1 be a sphere centered at(0, 1, -3) with radius 1 and let S2 be a sphere centered at (3, 5, -9) with radius 2. Find the distance between the two spheres. problem 2: Given three non-zero vectors v1, v2, v3 we say that they are mutually orthogonal when v1 dot v2= 0, v1 dot v3=0 ...
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