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. L

    Dot Product Rules Multiple choice

    Homework Statement See the image http://tinypic.com/r/33z6vz5/7 Homework Equations The rules of dot product multiplication. The Attempt at a Solution I've determined that 2 of the solutions are valid, while two of the choices are invalid. I thought C and D looked correct, making A...
  2. W

    V dot (dv/dt) = (0.5)*(d/dt)*(v^2) ?

    This is not a homework question, but a derivation in my class which I can't get around. Homework Statement Step1 F=ma Step2 \vec{F} = m\frac{d\vec{v}}{dt} Step3: Multiply both side by v \vec{F}.\vec{v} = m\vec{v}.\frac{d\vec{v}}{dt} Step4 Power = \frac{d}{dt}\frac{1}{2}m\vec{v}.\vec{v}...
  3. T

    What Conditions Make These Vector Dot Product Equations True?

    Homework Statement Under what conditions are the following true? a) |\mathbf{a}\cdot \mathbf{b}| =|\mathbf{a}||\mathbf{b}| b) (\mathbf{a} + \mathbf{b}) \cdot (\mathbf{a} - \mathbf{b}) = |\mathbf{a}|^2 - |\mathbf{b}|^2 Homework Equations None. The Attempt at a Solution a) I...
  4. S

    Linear algebra with dot product?

    Homework Statement Let A(theta)x = b for each theta in S. Calculate, (x dot b)/(|x||b|) A = [cos(theta) -sin(theta) sin(theta) cos(theta)] How is this related to theta? Recall that x dot y and |x| are the standard dot-product and magnitude, respectively, from vector-calculus...
  5. D

    Why is the Inducted Voltage Negative in Book B's Dot Convention?

    Hello, I have a doubt regarding dot convention in magnetically coupled circuits. In book A, the following is stated: But in book B, this is stated: In book B, why the inducted voltage of the second mesh (-j w M I1) has that negative sign ? According to dot convention, it is supposed that...
  6. R

    Prove nabla(a dot b): Freshman Seeks Help

    please prove : nabla(a dot b)=(b dot nabla)a+(a dot nabla)b+b cross nabla cross a+a cross nabla cross b; (a and b are all vectors) when I was proving it,I found it impossible to go from right side to left side. I don't know whether '(b dot nabla)a = b (nabla a)' is right or not , when...
  7. S

    Understanding Del Operation on Vector U Without Dot or Cross Product

    hi, I'm trying to follow a derivation in a paper and this equation is confusing me: (u'.\nabla)U = (\nablaU).u' Where U and u' are velocities. The operation of del on the vector U without a dot or cross product is giving me some grief. Can someone explain how this works to me...
  8. N

    How Is Work Calculated When Pulling a Wagon Up an Incline?

    A person pulls a wagon up an incline that makes an angled of 30 deg with the horizontal with a force on the handle of 30 pounds which makes an angel of 30 deg with the incline find the work done in pulling the wagon 100 ft 20cos30 will be a force along the surface of the incline and since...
  9. Z

    Vector dot product homework help?

    if A = 2i^+6k^ B=6i^+5j^ find A.B if A.B=0 then what do u conclude from it? one more question if A = 6i^+9k^ and B=-4i^+4j then find A+B,A-B,A.B
  10. S

    Integral of Complex exp of dot product

    S(\vec{q})= \int_0^r exp(i\vec{q}\cdot\vec{x})4\pi x^2 \ dx How would one approach this integral? I tried to "ignore" the dot product and proceeded with exp(i\vec{q}\cdot \vec{x})=exp(iqx) and got a wrong answer.
  11. K

    Prove Vector Derivative (using Dot Product)

    Homework Statement n. Let r1 and r2 be differentiable 3-space vector-valued functions. Directly from the definition of dot product, and the definition of derivative of vector- valued functions in terms of components, prove that d/dt (r1(t) • r2(t)) = r′1(t) • r2(t) + r1(t) • r′2(t). Homework...
  12. D

    Medical No problem! Glad to help jog your memory :)

    I have tried looking this up on the net without success. This is a (I think) classic psychology experiment in which subjects are asked to describe the movement of a small black stationary dot painted on a white wall. Some perceive the dot as stationary and others perceive that the dot moves...
  13. K

    Need clarification on dot convention for magnetically couped circuits

    i have started to use dot convention for magnetically circuit. my understanding is that if the currents for primary winding and current in the secondary winding are clockwise and the dots are ontop of the inductors then the mutual inductance value would be negative because the secondary winding...
  14. C

    Integrals with curl dot products

    Homework Statement 1. Evaluate \int_{S}\int curl F \cdot N dS where S is the closed surface of the solid bounded by the graphs of x = 4, z = 9 - y^2, and the coordinate planes. F(x,y,z) = (4xy + z^2)i + (2x^2 + 6y)j + 2xzk 2. Use Stokes's Theorem to evaluate \int_{C}F\cdot T dS...
  15. N

    Proof of Dot Product: X*X & X=0 Questions

    If X is an N vector, is it 1) possible for X*X to be negative? 2) if x*x=0, what is X. I am having trouble writing the proper proof. for 1 I stated that it is impossible for X*X to be negative bc if x is positive, X*X is positive and if x is negative, -X*-X is still positive. for 2 I...
  16. Q

    Vector product VS dot product in matrix

    hi, i don't really understand what's the difference between vector product and dot product in matrix form. for example (1 2) X (1 2) (3 4) (3 4) = ? so when i take rows multiply by columns, to get a 2x2 matrix, i am doing vector product? so what then is dot producT? lastly...
  17. 1

    Mastering Cross and Dot Products for Test Review

    i'm reviewing for a test and I can't remember how to do the cross product of (2A)x(3B) or how to find the angle theta when given components. or dot product: 2A . 3B
  18. S

    Is Triangle ABC a Right Triangle?

    Homework Statement Given triangle ABC with vertices A(4, 1, 7), B(-2, 1, 1) and C(-3, 5, -6)..is ABC a Right triangle Homework Equations The Attempt at a Solution I took the dot product of vertices A(4, 1, 7).B(-2, 1, 1), and it gives 0..but however I am a little confused, as...
  19. S

    In this case, the correct dot product is 22a.a + 15a.b - 3b.b.

    Homework Statement Expand and simplify: (2\vec{a} + 3\vec{b}) .(5\vec{a} - \vec{b} Homework Equations The Attempt at a Solution I tried expanding it, but was a little confused, and would really appreciate any help..would it be (2\vec{a})(\vec{a}) = 2 \vec{a}2? Thanks..
  20. 8

    Dot Product of G and A: Where Do the Denominators Go?

    Homework Statement what is the dot product of G{\bullet}A where A = \left(\frac{a_3}{l}-\frac{{a_1}}{h}\right) and G = 2{\pi}h{\frac{{a_2}}x{{a_3}}}{{a_1}{\bullet}{{a_2}}x{{a_3}}} Homework Equations The Attempt at a Solution The answer is zero and I've got the worked solution...
  21. W

    Dot product and cross product of vectors

    Homework Statement This isn't so much a problem of calculation, so much as it is I need to know if i did it right, you'll see what I mean. vectors v=(2,0,2), u=(-1,1,0), w=(0,-1,1) Computer the quantities that make sense (a period denotes the dot product, x denotes cross product)...
  22. V

    What are the values of s that make two given vectors orthogonal?

    By evaluating the dot product, find the values of the scalar s for which the two vectors b=X+sY and c=X-sY are orthogonal also explain your answers with a sketch: my working (X,sY).(X,-sY) has to equal 0 for them to be orthogonal x.x = 1 since they are unit vectors...
  23. E

    Exploring the Dot Product Expansion: Proving the Relationship between a and b

    Homework Statement Show that the dot product of vectors a and b is equal to 1/4|a+b|^2 - 1/4|a-b|^2 Homework Equations a dot b = |a||b|cos(theta) a dot b = a1b1 + a2b2 + ... The Attempt at a Solution I've tried using the combination of the cosine law and those two above dot...
  24. Ƒ

    Understanding Dot and Cross Products: Key Concepts Explained

    Not so much an actual problem, more like concepts. What exactly is the dot product? How about the cross product?
  25. H

    Determinant, dot product, and cross product

    I am reading through David Widder's Advanced Calculus and he abbreviates a determinant as: \left( \begin{array}{cccc} r_{1} \ s_{1} \ t_{1}\\ r_{2} \ s_{2} \ t_{2}\\ r_{3} \ s_{3} \ t_{3}\\ \end{array} \right) And refers to it by (rst). He then states...
  26. C

    Dot product of vector and symmetric linear map?

    Homework Statement My book states as follows: --- If u and v have the coordinate vectors X and Y respectively in a given orthonormal basis, and the symmetric, linear map \Gamma has the matrix A in the same basis, then \Gamma(u) and \Gamma(v) have the coordinates AX and AY, respectively. This...
  27. L

    Dot Product: Explaining 1/2 Coefficient

    OK, this has been bugging me for a while. Why is it that \mathbf{v} \cdot \frac{d \mathbf{v}}{d t} = 1/2 v^2 where regular v is just the magnitude of bold v or more specifically where does the 1/2 coefficient turn up.
  28. Rasalhague

    Dot product of 4-force and 4-velocity

    In what follows, I'll use bold for 4-vectors and an arrow over a letter to denote a 3-vector. I'll use a dot both for the Minkowski dot product and the Euclidean one, and multiplication of real numbers; the meaning in each case should be clear from the symbols on either side. \vec{v} and \vec{a}...
  29. T

    Dot product as matrix products?

    Why not make dot(u,v)=transpose(u)v rather than transpose(v)u?
  30. M

    Cross product and dot product of forces expressed as complex numbers

    Homework Statement I have came up with an example to illustrate my question. There is a rod, which can turn around p1. p1p2 = (-1+j) m p1p3 = (-3 + 3j) m p1p4 = (1 - j ) m F1 = (1+3j) N F3 = (-1 - 2j ) N F4 = unknown, orthogonal to the rod compute F2_n, orthogonal component of F2 to the...
  31. E

    Matrix multiplication and the dot product

    Homework Statement Suppose that A is an n x n matrix such that A(Transpose)A=I. Let x be any vector in R^n. Show that llAxll=llxll; that is, multiplication of x by A produces a vector Ax having the same length as x. Homework Equations Sqrt(x(transpose)x)=llxll The Attempt at a...
  32. C

    Why does the dot product use cosine?

    What is significance of the trig functions in both the cross and the dot product? I understand what the dot and cross products are, how they work, and what they give...but I don't understand why the dot product uses cosine and the cross product uses sine?
  33. T

    Dot product and cross product evaluation questions

    This question has a few parts. r = i + 2j + 3k s = 2i - 2j - 5k t = i - 3j - k Evaluate: a)(r.t)s - (s.t)r b)(r x s) x t. deduce that (r.t)s - (s.t)r = (r x s) x t can you prove this relative true for any three vectors a)(r.t)s - (s.t)r (r.t)s well I don't know...
  34. T

    Question about vectors and dot product.

    Hi, Can someone tell me if: -E dotted with ( A + B ) is equal to -E.A -E.B where E, A and B are all vectors What I mean is, does the minus sign appear on the E.B bit as well? Also, is \int \frac{d}{dt} (A) dV equal to: \frac{d}{dt} \int (A) dV Thank you
  35. U

    Maximum acceleration of a dot on a slinky?

    A dot (representing vibration) on a slinky exhibits simple harmonic motion as the longitudinal wave passes. The wave has an amplitude of 5,4 * 10^-3 m and a frquency of 4,0 Hz. Find the maximum acceleration of the dot. Please could you explain what equations to use and how to answer in...
  36. J

    Understanding Products in the Equation v^2 = u^2 + 2aS

    In the equation v^2 = u^2 + 2aS , What kind of products are v^2 , u^2 , and aS ? Cross product or dot product?
  37. D

    Calculating Integral of C F dot dr Using Stoke's Theorem

    Homework Statement Let C be the triangle from (0,0,0) to (2,0,0) to (0,2,1) to (0,0,0) which lies in th plane z=y/2. If F(x,y,z)=-3y^2i+4zj+6xk, calculate integral of C F dot dr using Stoke's Theorm. Homework Equations For the curl of F, I obtained -4i-6j+6yk. For N, I obtained...
  38. P

    Chemistry Lewis dot structures of complex molecules

    Homework Statement determine the electron dot structure of molecules a and b http://session.masteringchemistry.com/problemAsset/1144353/2/MMAt.05.067.jpgHomework Equations The Attempt at a Solution A) ::O: H | | H-C=N-HB) H | .. H-C-N=C=O:: | H I am not at all sure...
  39. W

    What Are Dot Products and Vector Cross Products in Mathematics?

    Can someone explain to me what a dot product and vector product of two vectors are? Be as detailed as possible please! And also why does the right hand rule for vectors work?
  40. E

    Force Vectors and Dot Products

    Hello all :smile:, I am interested in the following problem: In an ensemble of atoms, the forces on atom A and atom B are given by the vectors Fa=Fax+Fay+Faz and Fb=Fbx+Fby+Fbz, respectively. Their respective positions are given by, Pa=Pax+Pay+Paz and Pb=Pbx+Pby+Pbz I have two...
  41. E

    Forces Vectors And Dot Products

    Hello all :smile:, I am interested in the following problem: In an ensemble of atoms, the forces on atom A and atom B are given by the vectors Fa=Fax+Fay+Faz and Fb=Fbx+Fby+Fbz, respectively. There respective positions are given by, Pa=Pax+Pay+Paz and Pb=Pbx+Pby+Pbz I have two...
  42. O

    Dot Product, Derivative, and Vector Valued Functions

    Homework Statement Prove that, if \vec{r}(t) is a differentiable vector valued function, then so is ||\vec{r}(t)||, and \vec{r}(t) \bullet \vec{r'}(t) = ||\vec{r}(t)|| ||\vec{r}(t)||'Homework Equations I know how to do a dot product, but what bothers me is the fact that the question involves...
  43. W

    Need help with combination of dot product and cross product question

    Homework Statement Let \vec{A}, \vec{B}, and \vec{C} be three vectors which are all not in the same plane. Show that \vec{A}{\cdot}(\vec{B}{\times}\vec{C})=\vec{B}{\cdot}(\vec{C}{\times}\vec{A})=\vec{C}{\cdot}(\vec{A}{\times}\vec{B}) Homework Equations Don't know :( The Attempt at...
  44. A

    What is the Meaning of the Dot Product in Integrals?

    What does the following mean - \int \textbf{F} \cdot d \textbf{r} I know that its equal to work done. but i have problem in understanding it, what's the varibale. i am familiar with integrate cosxdx. what's is similar to dx in above equation. is it ds. Now how can one get to this from above...
  45. M

    Confusion regarding dot product of vectors(row matrices)

    I’ve got a confusion. We know a 1x3 row matrix is a 3-vector i.e. x= [ a b c] Matrix x can be written in vector notation like x= a i + b j + c k where i, j, k are unit vectors along x,y & z axes. For dot product of x.x = a2 + b2 + c2 when x= a i + b j + c k But according to...
  46. D

    Comparing Tensor Double Dot Scalar Product Definitions

    Ok I have seen the tensor double dot scalar product defined two ways and it all boils down to how the multiplication is defined. Does anyone know which is correct? I believe the first one is correct but I keep seeing the second one in various books on finite element methods. 1. \nabla \vec{u}...
  47. D

    Pale blue dot: what causes the bands?

    In the famous photo "Pale Blue Dot" of the Earth from outside the solar system, one can see "bands" of colour around the Earth. What causes these bands? Is that an optical illusion? Does the band in which Earth is found describe the Earth's orbit? What are the other coloured bands? What gives...
  48. T

    Dot product and cross product problem

    I am having problems with this questions my physics teacher gave us. Since he doesn't explain things well, I do not know how he got an answer of 66. Can you please explain to me how to get this answer? THX. For the following three vectors, what is C*(A X 3B) (the "*" is suppose to be a dot)...
  49. T

    Understanding the Dot Product of Derivatives

    Hi, Im having trouble understanding something in one of my Dynamics lectures. The lecturer said that: dr/dt dotted with d2r/dt2 (where r is a vector) equals: (1/2)(d/dt(dr/dt dotted with dr/dt))... I just can't get this result. I know it has something to do with the product rule...
  50. B

    Dividing vectors in dot products

    Homework Statement can you divide 2 vectors which are in fractions? Homework Equations example a . a / b . a (dot products) The Attempt at a Solution would it become a / b?
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