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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 (1,876 words) - 18:01, 29 August 2024
- ...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}{155 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 Force2 KB (271 words) - 08:02, 11 March 2008
- ...<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 tak13 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
- It is assumed that the initial square is the unit square with coordinates (0,0), (0,1), (1,0) and (1,1). Note that jumping al ...e original sequence). This inverse sequence may be applied verbatim to the unit square itself, which would result in an even smaller square of side length2 KB (333 words) - 18:16, 21 December 2015