What is Vector: Definition and 1000 Discussions

The VECTOR is a light all terrain tactical vehicle in service with the Royal Netherlands Army and Navy. The vehicle is produced by Dutch defense contractor Defenture.

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  1. hraghav

    Finding the x component of position vector

    I first calculated the time using y = (viy)(t) + 0.5gt^2 where y is the vertical displacement which is 0 for the ball landing back on the ground, viy is the initial vertical velocity ie 16.55m/s and g = -9.8m/s}^2. I get 2 values for t, t=0 and t= 3.377s. Then using the equation x = (vix)(t) =...
  2. chwala

    Find the magnitude and the direction of the resultant vector

    Going through this ( Revision) A salways your insights are quite helpful. I would like to go through all these questions; i will start with (5), ##\left( \dfrac {x} {y} \right)## = ##\left( \dfrac {10 \cos 40^0} {10 \sin 40^0} \right)## + ##\left( \dfrac {4 \cos 150^0} {4\sin 150^0}...
  3. Remle

    Vectors Directions: Where is this Resultant Vector Pointing?

    Ok. My problem is what angle to choose when adding vector. Statement does not tell me which one is the "first" force vector. So, when using the law of sine formula I get two results. First, using cosine to get the magnitude: $$\vec c = \sqrt{a^2 + b^2 +2ab\cos\theta},$$ $$\vec c = \sqrt{15^2 +...
  4. F

    I Finding position vector in general local basis

    How do you derive the position vector in a general local basis? For example, in spherical coordinates, it's ##\vec r =r \hat {\mathbf e_r}##, not an expression that involves that involves the vectors ## {\hat {\mathbf e_{\theta}}}## and ## \hat {{\mathbf e_{\phi}}}##. But how would you show this?
  5. T

    I Dimension of a vector space and its subspaces

    Can a vector subspace have the same dimension as the space it is part of? If so, can such a subspace have a Cartesian equation? if so, can you give an example. Thanks in advance;
  6. robotkid786

    Understanding E subscript R Notation in the Context of General Relativity

    All I know is that e subscript r must be a vector cos the book says so, but what does it mean, is it, a konstant in vector form? I'm confused by it (page one, chapter one spacetime and geometry by SeanCaroll) Help is appreciated Edit. Is vector r describing the curvature that takes place ?
  7. F

    How to define vectors in spherical coordinate system?

    I am extremely confused with how to represent vectors that do not start at the origin in spherical coordinate system. If they did start at the origin, the vector to any point is simply ##r\pmb{\hat{r}}##; however, what if it does not start at the origin as in the question above? One thing I can...
  8. MatinSAR

    Different forms of Stokes' theorem

    What am I trying to do for ##\vec V=\vec a \phi## : ##R.H.S= \oint \vec V \cdot d \vec \lambda=\oint \vec a \phi \cdot d \vec \lambda=\vec a \cdot \oint \phi d \vec \lambda ## ##L.H.S= \iint_S \vec \nabla \times \vec V \cdot \vec d \sigma=\iint_S \vec \nabla \times (\vec a \phi) \cdot \vec d...
  9. T

    I Why is the Cross Product Used in Mathematics? Understanding its Role and History

    So I do know that there does exist a generalization of the cross product (the exterior product), but this question does not concern that (and I would prefer it not ) I know that the cross product (that Theodore Frankel, for example, calls "the most toxic operation in math") works in 3D only...
  10. L

    Mathematica Plot gradient vector in ContourPlot

    Hi, I have made the following ContourPlot in mathematica and now I wanted to ##\vec{r}_1= \left(\begin{array}{c} -1 \\ 1 \end{array}\right)##, ##\vec{r}_2= \left(\begin{array}{c} 0 \\ \sqrt{2} \end{array}\right)## and ##\vec{r}_3= \left(\begin{array}{c} 1 \\ 1 \end{array}\right)## insert the...
  11. Slimy0233

    Calculating the flux of a vector field

    I am not sure why latex is not rendering, but here is the question. The answer is ##\frac{a^2}{8}## and for the love of my life, I don't know how. Can you please help me with this?
  12. Ineedhelpwithphysics

    Vector addition, trying to find the angle

    Is angle Vag 180 since the vector is a straight line pointing left? Also you can add 30 degrees with 150 which will be 180?
  13. Ineedhelpwithphysics

    Finding the magnitude (length) and direction (angle) of a vector

    So i found the magnitude which is (-1)^2 + (-2)^2 = P^2 = Sqrt(5) Then I used the inverse tan function to find the angle (direction) theta = arctan (-2/-1) = 63.8 degrees Im confused with my 63.8 degrees since the angle in the graph looks greater than 63.4 degrees I subtracted 180 by 63.8 and...
  14. Mohmmad Maaitah

    Solving 2-D vector along three directions (say at 0,60 and 120 degree)

    So for 1 I know it's Yes you can, but I don't understand what uniquely means here so I can't say if it's uniquely or not. for 2 I've never seen a 2-D vector broken into 3 reference axies so I guess No? What really confuse me is the answers which goes 1-C and 4-A
  15. Mohmmad Maaitah

    Diffrence between resolving vector to components and find projections

    I don't get what is the difference when I am asked to re-solve components and find projections to axes other than the Y and X I know that the parallelogram works for the first one and the dot product for the second but what's the diffrence!
  16. C

    Needs clarity on this displacement vector diagram

    The problem is actually a solved example My attention is focused in understanding the displacement vector diagram as it has to deal with question (iv). I have no problem understanding the velocity vector sketch below: As you can see ND is the velocity of the river current due East and NE is...
  17. Skaiserollz89

    Symmetry of an Integral of a Dot product

    This homework statement comes from a research paper that was published in SPIE Optical Engineering. The integral $$\int\int_{-\infty}^{\infty}drdr'W(\vec{r})W(\vec{r'}) \vec{r} \cdot \vec{r'}=0$$ is an assumtion that is made via the following statement from the paper : "Since...
  18. chwala

    Finding the projection of a Vector

    I am looking at this now; pretty straightforward as long as you are conversant with the formula: anyway i think there is a mistake on highlighted i.e Ought to be ##-\dfrac{15}{37}(i+6j)## just need a confirmation as at times i may miss to see something. If indeed its a mistake then its time...
  19. R

    B Define a vector that transfers the reference systems to the future

    Suppose a stationary reference frame, any other reference frame will have a clock that advances at t'= t/gand is moving away at velocity v. g is the relativistic factor. we can write: C d t' = Cdt/g and d x = v dt this can be written (Cdt',Cdx)=(C/g,C v) dt ; since 1/g2+ v2 =...
  20. L

    I Parallel vector, I need a bit of explanation

    Given that c = 3i + 4j and d = i - 2j, find u if uc + d is parallel to i + 3j, this is the question in the solution, it says that we have to multiply the 3 with the i i do know that this is the ”method“ to do this question but I’d like a bit of explanatio. I don’t understand why the 3 is...
  21. Slimy0233

    I Need Help understanding Griffiths [Vector Analysis]

    I don't understand anything about how 1.18 came to be (Red Rectangle), any help would be greatly appreciated!
  22. susan_khan

    Airplane Vector Problem: Drawing the diagram

    An airplane has an air velocity of 500 km/h [N 30 E] and encounters a wind from [S 75 W] at 180 km/h, find the ground velocity. Make sure you draw a big, labelled diagram. Please help! I’m understand the calculations that need to be done (cosine law then sine law for the angle) but I’m a little...
  23. Gardunf070

    Find unknown wind velocity given airlplane's speed

    But I don't understand how is that it ends up on the west side if both vectors were pointing east.
  24. E

    Vector is a function of its position or not?

    At first I thought that this force vector ## \vec F = 3 \hat x + 2 \hat y ## is a function of ## x ## and ## y ##, which is to say that its magnitude and direction vary with the x and y positions, but this is not so, right? It's just a force with a constant magnitude and direction. And I can...
  25. T

    I Understanding Vectors: Magnitude & Direction

    Good Morning (And apologies if this is not the right forum -- it is not a homework problem.) On the one hand, a vector is an arrow and a tail: it has magnitude and direction. It is used to describe direction, forces, acceleration, etc. However, there are more mathematical definitions: a...
  26. CaliforniaRoll88

    Multi-part question involving a vector field

    (a) ##\vec G=24xy\hat a_x+12(x^2+2)\hat a_y+18z^2\hat a_z## @ ##P(1,2-1)## ##\vec G=24(1)(2)\hat a_x+12(1^2+2)\hat a_y+18(-1)^2\hat a_z## ##\vec G=48\hat a_x+36\hat a_y+18\hat a_z## (b) I am not sure how to get this part started. Could someone point me in the right direction?
  27. chiyu

    I Vector calculus: line element dr in cylindrical coordinates

    We were taught that in cylindrical coodrinates, the position vector can be expressed as And then we can write the line element by differentiating to get . We can then use this to do a line integral with a vector field along any path. And this seems to be what is done on all questions I've...
  28. C

    Finding vectors parallel to a given vector

    For (b) of this problem, The solution is, However, I am confused why the two parallel vectors are ##(\frac{2}{\sqrt{13}}, \frac{3}{\sqrt{13}})## and ## (-\frac{2}{\sqrt{13}}, -\frac{3}{\sqrt{13}}) ## should it not be ##(2,3)## and ##(-2,-3)##. Do somebody please know why they wrote that? Also...
  29. whartung

    I Solving simultaneous vector equations

    I'm sorry, this touches so many areas, I just didn't know which pigeon hole to put it in, so I dropped it here in General. Simple summary. I have two physics equations. The problem I'm trying to solve is a follower is chasing a target that is moving at a fixed velocity. The follower is going...
  30. C

    Does each norm on vector space become discontinuous when restricted to S^1?

    Dear Everybody, I am having trouble with last part of this question. I believe the answer is no. But I have to proof the general case. Here is my work for the problem: Suppose that we have two distinct norms on the same vector space ##X## over complex numbers. Then there exists no ##K## in...
  31. entropy1

    B How to multiply matrix with row vector?

    How do I calculate a 3x3 matrix multiplication with a 3 column row vector, like below? ## \begin{bmatrix} A11 & A12 & A13\\ A21 & A22 & A23\\ A31 & A32 & A33 \end{bmatrix}\begin{bmatrix} B1 & B2 & B3 \end{bmatrix} ##
  32. MatinSAR

    Vector Calculus in 1D: ± to Show Magnitude?

    [mentor's note - moved from one of the homework help forums] Homework Statement:: It's a question. Relevant Equations:: Vector calculus. Is it true to say that in one dimension I can show vector quantities using ±number instead of a vector? ± can show possible directions in one dimension and...
  33. O

    I Dot product of two vector operators in unusual coordinates

    Hi. I hope everyone is well. I'm just an old person struggling to make sense of something I've read and I would be very grateful for some assistance. This is one of my first posts and I'm not sure all the LaTeX encoding is working, sorry. Your help pages suggested I add as much detail as...
  34. sHatDowN

    Vector sample problem -- Force components on a spring mechanism

    Determine the amount and type (tensile or compressive) of the spring force so that the resulting force is a vertical force. Also get the resultant force. i find 60N (compressive) and resultant forces is 10800 is that correct?
  35. sHatDowN

    Vector problem, magnitude of the force

    Member CB of the vise shown exerts on block B a force P directed along line CB. Knowing that P must have a (1237) N horizontal component, determine (a) the magnitude of the force P, (b) its vertical component i don't get it what the "N horizontal component"
  36. sHatDowN

    Simple Addition of Vector Forces on an Eye-Hook

    The screw eye is subjected to two forces, F1 and F2. Determine the magnitude and direction of the resultant force.
  37. K

    4- vector potential transformation

    What is 4- vector potential transformation under Gauge fixing ?
  38. R

    A Converting this vector into polar form

    In the following%3A%20https://pubs.rsc.org/en/content/articlehtml/2013/sm/c3sm00140g?casa_token=3O_jwMdswQQAAAAA%3AaSRtvg3XUHSnUwFKEDo01etmudxmMm8lcU4dIUSkJ52Hzitv2c_RSQJYsoHE1Bm2ubZ3sdt6mq5S-w'] paper, the surface velocity for a moving, spherical particle is given as (eq 1)...
  39. R

    Sum of angles with x,y and z axis made by a vector

    I want to know if there is any proper relation between the angles of a vector with the three dimensional coordinate axes, if the angles are ,α , β and γ, will the sum of α, β and γ be 180 degress that is α + β + γ = 180°,m finding the same to be true in a 2 D case where α + β = 90° and γ =...
  40. G

    I 4-Current vector potential transformation under Gauge fixing

    I am given an initial vector potential let's say: \begin{equation} \vec{A} = \begin{pmatrix} g(t,x)\\ 0\\ 0\\ g(t,x)\\ \end{pmatrix} \end{equation} And I would like to know how it will transform under the Lorenz Gauge transformation. I know that the Lorenz Gauge satisfy...
  41. P

    C/C++ Overload functions by dimension of vector

    vector<OP> negate (vector<OP> a) { a.insert(a.begin(), neg); return a; } vector<vector<OP>> negate (vector<vector<OP>> a) { for (int i=0; i<a.size(); i++) a[i] = negate(a[i]); // reference to 'negate' is ambiguous? return a; } OP is an enum here. Why can't C++...
  42. H

    Unitary vector commuting with Hamiltonian and effect on system

    Hi, I'm not sure to understand what ##| \phi_n \rangle = \sum_i \alpha_i |\psi_n^i## means exactly or how we get it. From the statement, I understand that ##[U,H] = 0## and ##H|\psi_n \rangle = E_n|\psi_n \rangle## Also, a linear combination of all states is also an solution. If U commutes...
  43. K

    Complex Matrix in vector norm

    TL;DR Summary: For every Complex matrix proove that: (Y^*) * X = complex conjugate of {(X^*) * Y} Here (Y^*) and (X^*) is equal to complex conjugate of (Y^T) and complex conjugate of (X^T) where T presents transponse of matrix I think we need to use (A*B)^T= (B^T) * (A^T) and Can you help...
  44. binbagsss

    I Using the Chain Rule for Vector Calculus: A Tutorial

    This is probably a stupid question, but I have never realised that there's an order things should be done in the chain rule , so for example ## \nabla(\bf{v}.\bf{v})=2\bf{v} (\nabla\cdot \bf{v}) ## and not ## 2 \bf{v} \cdot \nabla \bf{v} ## Is there an obvious way to see / think of this...
  45. C

    Discovering Vector Direction in Conservation of Energy Problems

    For this problem, Is the length vector into or out of the page and how do you tell? EDIT: Why must we use conservation of energy for this problem? I tried solving it like this: ##IdB\sin90 = ma ## ##IdB = ma ## ##v_f = (2aL)^{1/2} ## ##v_f = (\frac {2dIBL} {m})^{1/2} ## Which is incorrect...
  46. S

    I Can time be another basis vector under Galilean relativity?

    I refer to the video of this page, where there is a description of Galilean relativity that is meant to be an introduction to SR, making the comprehension of the latter easier as a smooth evolution from the former. All the series is in my opinion excellent, but I think that this aspect is...
  47. nataelp

    Force between 2 point charges in VECTOR format (x i + y j + z k)

    I tried using the distance between r2 and r1 and plugging them into the equation for i, j, k. >> So for the force in the x direction it was k*(4E-6*4E-6)/(4-9)^2. The answer I got was wrong according to webassign. Can someone please tell me what I am missing?
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