What is Vector notation: Definition and 66 Discussions

In mathematics and physics, vector notation is a commonly used notation for representing vectors, which may be geometric vectors, or, more generally, members of a vector space.
For representing a vector, the common typographic convention is lower case, upright boldface type, as in v. The International Organization for Standardization (ISO) recommends either bold italic serif, as in v, or non-bold italic serif accented by a right arrow, as in






v
→





{\displaystyle {\vec {v}}}
.In advanced mathematics, vector are often represented in a simple italic type, like any variable.

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  1. patric44

    Confusion about four vector notation

    hi guys I am trying to learn special relativity and relativistic quantum mechanics on my own and just very confused about the different conventions used for the notation!?, e.g: the four position 4-vector some times denoted as $$ x_{\mu}=(ct,-\vec{r})\;\;or\;as\;x_{\mu}=(ict,\vec{r}) $$ or...
  2. Anonymous1

    B Vector Notation: Italic Boldface Symbolization

    is it true that vectors are symbolised as an italic boldface 'a'
  3. lboulden

    Unit vector notation, why use 3 letters for a component?

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  4. J

    I Element-wise square root of a vector notation?

    What is the notation to show element-wise square root of a vector or matrix?
  5. M

    I Vector Notation of Quantum States for 2 Qubit System

    I am confused about the vector notation of quantum states when I have a 2 qubit system. For 1 qubit, I just write l1> = (0 ;1 ) for representing 1, and l0> = (1;0) for representing 0. Dirac notation is straightforward However when it comes to representing two qubits in linear algebra I...
  6. R

    Can I Use Vector Notation for Graph Translations?

    Homework Statement Hi. Its not really a problem but just a general question. When doing graph translations, such as move the parabola x units right or y units up etc, Is it okay to use vector format. So instead of saying move this equation 4 units left, could you write it like this -> <-4,0>...
  7. E

    Finding the net gravitational force with Vector Notation

    Information Given: In the figure, a square of edge length 17.0 cm is formed by four spheres of masses m1 = 4.70 g, m2 = 2.90 g, m3 = 0.800 g, and m4 = 4.70 g. Question: In unit-vector notation, what is the net gravitational force from them on a central sphere with mass m5 = 2.90 g? Attempted...
  8. T

    Vector Notation in Nolting Theoretical Physics 1

    On pg. 60 of Nolting Theoretical Physics 1 for the definition of a vector multiplied by a scalar the book shows two little up arrows if the scalar is greater than zero and an little up arrow and then a little down arrow if the scalar is less than zero. Then again on pg. 61 for definition 1.139...
  9. Y

    I What does this vector notation mean?

    Hello, I'm currently doing vectors in class, but I don't know what these parts mean. Especially φ(a,b). I understand cos(φ), but I don't understand cos(φ(a,b)). φ is the angle between two vectors a and b, but what does the (a,b) part add? I tried to google, but I couldn't really find...
  10. binbagsss

    A Killing vector notation confusion time translation

    Okay so when there is time-translation symmetry because the metric components do not have any time- dependence, ##\partial_x^0## is a Killing vector. I'm just confused what this means explicitly, since a derivative doesn't make sense without acting on anything really? But by 'spotting the...
  11. Iron_Man_123

    Body diagonals -- unit vector notation

    Homework Statement I'm fully convinced that the zero values make sense, yet they are wrong, can somebody please explain why is that the case Homework Equations N/A The Attempt at a Solution Attempt in the image above
  12. S

    I How Do Tensor and Vector Notations Differ in Physics?

    Hello. I am confused about the notation for tensors and vectors. From what I saw, for a 4-vector the notation is with upper index. But for a second rank tensor (electromagnetic tensor for example) the notation is also upper index. I attached a screenshot of this. Initially I thought that for...
  13. snoopies622

    I Confused about basis vector notation

    Why are basis vectors represented with subscripts instead of superscripts? Aren’t they vectors too? Isn’t a vector a linear combination of basis vectors (and not basis co-vectors?) In David McMahon’s Relativity Demystified, he says, “We will often label basis vectors with the notation e_a...
  14. J

    Find Resultant Displacement Vector in Unit Vector Notation

    1. The problem statement, all variables and given/known dat A car travels 20 mi at 60 degrees north of west, then 35 mi at 45 degrees north of east. Express each displacement vector in unit vector notation. Take the +x-axis due east and the +y-axis due north. Use the component method to obtain...
  15. J-dizzal

    Understanding Vector Notation: The Role of i, j, and k as Standard Unit Vectors

    Could anyone clarify what is the name of the i,j,k notation for vectors if there even is one?
  16. R

    Value of an unusual vector notation

    Homework Statement If a,b,c are three -zero vectors such that each one of them are perpendicular to the sum of the other two vectors, then the value of | a, b, c|2 is |a|2 + |b|2 + |c|2 |a| + |b| + |c| 2(|a|2 + |b|2 + |c|2) ½(|a|2 + |b|2 + |c|2) Homework Equations a.b = ab cosθ |axb|= ab sinθ...
  17. M

    MHB Using vector notation describe a triangle

    Hey! :o Using vector notation describe a triangle ( in space ) that has as vertices the origin and the endpoints of the vectors $\overrightarrow{a}$ and $\overrightarrow{b}$. Could you tell me what I am supposed to do?? (Wondering)
  18. C

    Velocity function, unit vector notation, acceleration, speed

    The problem: The velocity ~v (vector notation, don't know how to type) is given by: ~v = (6.0t - 4.0t^2)ˆi + 8.0ˆj + (3.0t) with |~v| in meters per second and positive t seconds. ˆi, ˆj, ˆk have their usual meanings (unit vector notation). (a) What is the acceleration ~a of the particle when...
  19. Roodles01

    Lorrentz force law & vector notation

    Homework Statement A current element is 3.0mm long, centerd on the origin of cartesian coordinates, and carries a current of 2.5A in the direction ez. What field does it produce at the point (3.0, 0, 4.0) Homework Equations This is obviously a Lorentz force law question so . . . ∂B =...
  20. ThomasMagnus

    Integrating Velocity When in Unit Vector Notation

    Homework Statement Say for example, a particles velocity was given by the following equation: \vec{V}(t) = (2t2-4t3)\hat{i} - (6t +3)\hat{j} + 6\hat{k} If I wanted to find the displacement of the particle between t=1s and t=3s, could I just integrate like this? \int \vec{V}= (2t3/3...
  21. cactusblanket

    Acceleration of a Charged Particle in 3D Vector Notation

    Homework Statement Hi there! Here is a problem from our 1st year course. We have covered the basics on charges and Coulomb's Law. However our prof said he designed the following question to be "deliberately obscure"! Two charges of 4.00μC are fixed in space, Q1 at (0,0,0) and Q2 at...
  22. R

    Working with Bra and Ket vector notation

    I have 2 ket vectors that i need to prove are orthogonal and normalised I know <Up|Down> = <Down|Up> = 0 <---- Orthogonal Condition I know <Up|Up> = <Down|Down> = 1 <---- Normalisation Condition My problem is I have 2 ket vectors, say |A> and |B>, containing |Up> and |Down> terms. How do I...
  23. M

    Vector notation - form versus vector?

    Hi there, During a recent tutorial, I asked my tutor about the notation he uses for vectors - he draws the little half arrow above them and I was curious whether that was significant, as opposed to just underlining vectors. He said it was a mathematical technicality and suggested I look up...
  24. K

    How Do You Write Position Vectors in Unit Vector Notation?

    Homework Statement A steel ball is fired from a ballistic launcher at different angles. The launched ball has been found to travel from the edge of a table to land 30.0 cm from the far end of the table when starting from the height of the table and launched at an angle of 30.0◦ above the...
  25. W

    Some help with set and vector notation, please

    Preface note: the R and Z in the {}s below should be double-struck, but I couldn't figure out how to do that here. I tried the usual shortcuts to no avail. I am writing pseudo-code for a publication, and am asked to use rigorous math notation, which is new to me. I am trying to express the...
  26. X

    Writing impulse in vector notation

    Homework Statement A baseball strikes a bat. It's moving at 40m/s to the left horizontally. When it hits the bat it leaves at 60m/s with an angle of 30 degrees to the horizontal. The mass of the ball is 0.25kg. Homework Equations P(momentum)=mv Pf-Pi=ΔP ΔP=J(impulse) The Attempt at a Solution...
  27. J

    Calculating Work with Vector Notation

    Homework Statement A force F=12NÎ-10NĴ acts on an object. How much work does this force do as the object moves from the origin to the point R=13mÎ+11mĴ? Homework Equations Work is the product of Force and Displacement (W=F*s) The Attempt at a Solution Things I know, or think I know: The object...
  28. W

    Vector Notation for Work: An Exploration of Force and Displacement

    Homework Statement Homework Equations Work = F* delta x The Attempt at a Solution My thought process since the force is given in vector notations multiply the pair of i components together same applies with j and k components. However this process actually strangely does not...
  29. H

    Vector Notation, arrow coupled with hat versus hat alone

    I've attached the .pdf from which I have questions. After it says "Take the square of the numerator" halfway down the page, there is an equation that lists vector components with hats and arrows at the same time, and the arrow on other vectors. Can someone help explain the difference to me...
  30. T

    Vector notation / manipulation question

    Homework Statement Xuv is a 4x4 tensor and Vu is a vector. Vu = (-1, 2, 0, -2) (i.e. it is a 1x4 vector). Find the quantities Vu Vu and Vu Xuv Homework Equations Given above The Attempt at a Solution I'm having trouble finding Vu. Initially I thought that it should be the...
  31. D

    Work on unit vector notation for matrices?

    I would like to inquire whether there has been any recent work on representing matrices in unit vector notation? Thanks in advance!
  32. L

    Vector Notation Inconsistencies

    My teacher writes 3 dimensions like this: My textbook writes it like this: If my online H/W is not directly written by my teacher and not directly written by my textbook (MasteringPhysics online HW), then when presented with a vector such as: A = (2,1,-4) Should I read...
  33. nukeman

    Vector Notation with force and displacement help. Thanks

    Homework Statement This is not a homework question, but rather a review question. I have the answer, ill post below, but have no idea how to get to the answer :) Question: "A constant force of 90.0N acts on a ball while it has a displacement of 1.40m at 10 degrees below the x-axis. The...
  34. J

    Very quick question about vector notation

    Homework Statement http://people.math.carleton.ca/~mezo/A5math1102-11.pdf number one Homework Equations The Attempt at a Solution What does Z5/5 mean?
  35. O

    Help with Vector Notation: \partial_{\mu} \phi^{*}\partial^{\mu} \phi

    Not a particularly direct question, just something I don't mathematically understand and would very much appreciate help with. For some scalar field \phi, what would \partial_{\mu} \phi^{*}\partial^{\mu} \phi mean in mathematical terms. ie how would I calculate it? From what I understand...
  36. S

    F=ma, kinematics in vector notation

    I'd like to go over my approach to a question I am doing right now, but I've posted my general approach instead of the question itself. Say there is some object with three forces acting on it, and these forces are given to me in vector notation (i.e. with unit vectors "i" and "j"). I am also...
  37. 1

    Unit Vector Notation Addition

    Homework Statement Consider the following vectors: a = (5.0m) i + (2.0m) j b = (-14m) i + (6.0m)j Sum of a+b in unit vector notation? Homework Equations The Attempt at a Solution I'm not sure about this notation, all I know about adding vectors is graphically. Does (5.0m)...
  38. S

    Understanding Vector Notation: Solving Homework Equations

    Homework Statement Does r_{12} mean distance from point 1 to point 2, or point 2 to point 1?Homework Equations The Attempt at a Solution
  39. G

    Which notation is the proper way to write vector quantities?

    What' the proper way to write vector notation? For a force... (10 N)i + (5 N)j + (6 N)k or are the brackets not standard and I can just go like this when I can indicate the superscript arrow above the unit vectors 10 Ni + 5 Nj + 6 Nk I'm not exactly sure and was hoping someone could tell...
  40. W

    Euler-Lagrange equation in vector notation

    I read in hand and finch (analytical mechanics) that if you assume you have a lagrangian: L=(\phi,\nabla\phi,x,y,z) Then what does the euler lagrange equation look like in vector notation. I know that if you have a function with more than 1 independent variable then the euler-lagrange...
  41. G

    Work done by force (Vector notation)

    Homework Statement How much work is done by a force= (2x)i N + (3)j N with x in meters, that moves a particle from a position (initial) = (2m)i + (3m)j to a position (final) = (-4m)i + (-3m)j? Answer: - 6 J Homework Equations Work = integral of Force The Attempt at a Solution...
  42. U

    Why does the P come before the Q in relative displacement vector notation?

    We have 3 points. O, P, Q. OP = rP OQ = rQ but why is QP PrQ rather than QrP? I'm just starting M4 and I really like to understand everything. This doesn't make any sense to me and I can't find out online. I'm sure there's a logical reason for it to be like that. Is it because you go...
  43. T

    Which Vector Notation is Best for Physics, Engineering, and Mathematics?

    I'm curious, which vector notation is preferred by physicists/engineers/mathematicians? In linear algebra we used matrix notation exclusively, putting the x,y,z,... components down a column matrix. (no idea how to put this in latex). In all my other courses though, we've been using (xi +yj...
  44. B

    Write Tr = T1 + T2 in vector notation

    Problem is here http://engineeringhomework.net/statics/hw1p19.html" I understand that Tr=T1+T2, but the different axis is throwing me off.
  45. V

    Torque in Unit Vector Notation

    Homework Statement Homework Equations Torque is equal to the derivative of angular momentum with respect to time The Attempt at a Solution I took the derivative of each function given in parts a - d and plugged in the value for t to get my answer for the torque. I don't quite...
  46. A

    Circular Motion with Vector Notation

    Homework Statement A particle is in uniform circular motion about the origin of an xy coordinate system, moving clockwise with a period of 7.00 s. At one instant, its position vector (from the origin) is r = (6.00 m) i - (3.00 m) j. At that instant, what is its velocity in unit-vector...
  47. J

    Quick vector notation question

    Homework Statement My prof has written out a derivation which says: \vec{a_{t}} = α x \vec{r} Why does everything except α have a vector sign on it? I think α should be a vector here too... By the way, he also derived dv/dt = ω, and v had a vector symbol but ω did not. Is that right...
  48. B

    Does the Subscript x=0 Indicate a Zero x-Component in Vector Notation?

    I have a quick question to ask you guys. In the first problem found http://whites.sdsmt.edu/classes/ee382/homework/382Homework4.pdf" , does the vertical line with the subscript x = 0 mean that the x-component of the vector is always 0? If so, then I could just remove the x-component from the...
  49. L

    Grad of a function in vector notation

    Homework Statement q = xy^{2}z i + y^{2}xz j + e^{2z} k Homework Equations Grad (f) = (fx,fy,fz), where fx, fy, fz are partial derivatives The Attempt at a Solution I am Comptent at computing the gradient of a function, however i do not see how to do this when in vector...
  50. T

    Using Vector Notation in Physics: Appropriate or Wrong?

    I have a general question on presenting physics work: When is it appropriate to use vector (bold) notation? I understand the difference between vectors and scalar quantities, and always used to think an equation with a vector on the LHS needed to have a vector on the RHS, but in writing up a...
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