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  • Its vector formulation states that for any vectors <math>\overrightarrow{v}</math> and The full Cauchy-Schwarz Inequality is written in terms of abstract vector spaces. Under this formulation, the elementary algebraic, linear algebraic,
    13 KB (2,048 words) - 14:28, 22 February 2024
  • ...lso most abstractly, a vector is any object which is an element of a given vector space. ...\,y\,\,z\,\,...)</math>. The set of vectors over a [[field]] is called a [[vector space]].
    11 KB (1,875 words) - 14:35, 7 January 2025
  • ...mber [[zero (constant) | 0]], while a point two units to the right and one unit down from the origin corresponds to the complex number <math>2 - i</math>. * [[Vector]]
    902 bytes (135 words) - 00:23, 14 November 2024
  • P=s*markscalefactor*unit(A-B)+B; R=s*markscalefactor*unit(C-B)+B;
    6 KB (947 words) - 19:44, 26 November 2021
  • We consider the [[vector]] equation of the diagonal segment represented by: ...internal diagonal have a length of <math>d</math>. The point enters a new unit cube in the <math>x,y,z</math> dimensions at multiples of <math>\frac{d}{15
    5 KB (923 words) - 20:21, 22 September 2023
  • Let the circumcenter be represented by the vector <math>O = (0, 0)</math>, and let vectors <math>A,B,C</math> correspond to t ...>\vec O = \vec X(3)</math> as origin and <math>\vec {HO}</math> as a unit vector.
    59 KB (10,203 words) - 03:47, 30 August 2023
  • We shall present a standard triangle inequality proof as well as a less-known vector proof: ===Vector Proof (Due to Titu Andreescu and Oleg Mushkarov)===
    4 KB (769 words) - 15:07, 29 December 2019
  • ...newton]]. Force has [[direction]] as well as [[magnitude]], meaning it's a vector.
    1 KB (184 words) - 01:37, 24 November 2024
  • ...th>, it's momentum must approach <math>\infty</math>, so the [[force]] per unit [[time]] (i.e. inpulse, or change in momentum) needed to increase the speed This means if a body moves such that it's momentum vector remains invariant with time then we can conclude that there is no net Force
    2 KB (271 words) - 08:02, 11 March 2008
  • '''Velocity''' is a [[vector]] quantity, defined by the speed at which an object is traveling (its magni ...r, velocity can be considered as the product of speed and the unit tangent vector -- the instantaneous direction of the object.
    493 bytes (76 words) - 20:36, 14 January 2025
  • ...<math>\angle CDE=\angle DEA=90^o</math>. This means that there exists some vector <math>DE</math> parallel to the plane of <math>ABC</math> that forms two ri .... Also, because the i unit vector must be orthogonal and also 0. Thus, the vector of line <math>DE</math> is simply <math>2tj+2k</math>
    3 KB (470 words) - 18:46, 17 July 2023
  • ...ive]] of [[displacement]], is defined to be the change of [[velocity]] per unit time at a certain instance. ...ac{\textbf{v}_2 -\textbf{v}_1 }{t_2 - t_1}</cmath> Note that velocity is a vector, so the magnitudes cannot be just subtracted in general.
    2 KB (277 words) - 13:04, 24 April 2022
  • Time is the vector component of measuring durations of events. The SI unit for time is the second, which is abbreviated with "s" or "sec."
    148 bytes (26 words) - 17:43, 7 December 2024
  • ...row{OP_1}, \overrightarrow{OP_2}, \ldots, \overrightarrow{OP_n}</math> are unit vectors such that points <math>P_1, P_2, \ldots, P_n</math> all lie in a pl ...th>\left\vert \overrightarrow{OM} \right\vert</math> denotes the length of vector <math>\overrightarrow{OM}</math>.
    3 KB (602 words) - 14:44, 29 January 2021
  • //dir(25) is a unit vector pointing 25 degrees //put a label at the end of the 75 degree unit vector (and position it out 75 degrees)
    16 KB (2,317 words) - 02:54, 24 October 2014
  • ...nd <math>C</math> are all unit vectors because all those points are on the unit sphere. ...ints <math>N</math>, <math>A</math>, <math>B</math>, and <math>C</math> as unit vectors with their coordinates.
    6 KB (1,013 words) - 21:09, 21 November 2023
  • //dir(25) is a unit vector pointing 25 degrees //put a label at the end of the 75 degree unit vector (and position it out 75 degrees)
    2 KB (272 words) - 00:43, 23 October 2014
  • ...no two of <math>x</math>, <math>y</math>, and <math>z</math> are within 1 unit of each other is greater than <math>\frac {1}{2}</math>. What is the smalle ...les is just a translation of each <math>(x_{1},\dotsc,x_{k})</math> by the vector <math>(0,1,\dots,k-1)</math>; in the above solutions, it corresponds to tak
    13 KB (2,131 words) - 16:24, 11 October 2024
  • ...}{2}</math>. The z-coordinate of the plane never exceeds the height of the unit cube for <math>0 \leq x \leq 1, 0 \leq y \leq 1</math>. Therefore, the volu ....5,0]}\times\vec{[0,1,.5]}=\vec{[.25,-.5,1]}</math>). We can multiply this vector by <math>-4</math> to make things look cleaner and get <math>\vec{[-1,2,-4]
    10 KB (1,592 words) - 12:35, 4 April 2024
  • ...ath>z^2</math> is in the opposite direction of <math>1+2i</math>. The unit vector in the complex plane in the desired direction is <math>\frac{-1}{\sqrt{5}}
    3 KB (428 words) - 01:34, 31 December 2020

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