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• Cauchy-Schwarz Inequality
  ...ion shows that <math>\mathbf{p}</math> and <math>\mathbf{q}</math> form an orthogonal basis of the linear subspace spanned by <math>\mathbf{u}</math> and <math>\ ...s established that <math>\mathbf{p}</math> and <math>\mathbf{q}</math> are orthogonal, and that the sum of their squared norms is <math>1</math>. Now we have
  13 KB (2,048 words) - 15:28, 22 February 2024
• 2003 AIME II Problems/Problem 11
  Let <math>N</math> be the orthogonal projection from <math>C</math> to <math>AB.</math> Thus, <math>[CDM]=\frac{
  5 KB (772 words) - 19:47, 1 August 2023
• Finite Fourier Analysis
  ...ove that the set of eigenvectors {<math>{f_n : n=0,\ldots, N-1}</math>} is orthogonal, and that the norm of <math>f_n</math> is <math>\sqrt{N}</math>. We can no
  4 KB (724 words) - 19:15, 9 September 2006
• 2007 USAMO Problems/Problem 6
  ...>, <math>F</math>. Since <math>IE\perp AE</math>, <math>\omega</math> is [[orthogonal]] to the inversion circle, so <math>\mathcal{I}(\omega)=\omega</math>. Cons
  7 KB (1,274 words) - 15:11, 31 August 2017
• 2007 Cyprus MO/Lyceum/Problems
  The volume of an orthogonal parallelepiped is <math>132\;\mathrm{cm}^3 </math> and its dimensions are i In the following figure <math>ABCD</math> is an orthogonal trapezium with <math>\ang A= \ang D=90^\circ</math> and bases <math>AB = a<
  13 KB (1,990 words) - 08:29, 19 December 2009
• 2007 Cyprus MO/Lyceum/Problem 10
  The volume of an orthogonal [[parallelepiped]] is <math>132\;\mathrm{cm}^3 </math> and its dimensions a
  969 bytes (139 words) - 16:47, 6 May 2007
• 2007 Cyprus MO/Lyceum/Problem 22
  In the figure, <math>ABCD</math> is an orthogonal trapezium with <math>\angle A= \angle D=90^\circ</math> and bases <math>AB
  979 bytes (166 words) - 02:33, 19 January 2024
• De Longchamps point
  ...rthogonal to the <math>\omega_C.</math> Prove that de Longchamps circle is orthogonal to the <math>\omega_A, \omega_B, A-</math>power, <math>B-</math>power and <
  10 KB (1,780 words) - 09:23, 17 November 2022
• 1995 AHSME Problems/Problem 30
  ...32,\frac 32\right)</math>. The plane that passes through this point and is orthogonal to the diagonal has the equation <math>x+y+z=\frac 92</math>.
  5 KB (828 words) - 05:52, 30 September 2023
• 2007 AMC 12B Problems/Problem 25
  ...n, the k unit vector must be zero. 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
  3 KB (470 words) - 19:46, 17 July 2023
• 2002 USAMO Problems/Problem 6
  ...tial blocks (5 oriented the same way, including itself, and 9 oriented the orthogonal way). Therefore <math>14b(n)\geq 2n(n - 2)</math> or
  5 KB (940 words) - 17:33, 16 July 2014
• 2004 AMC 12B Problems/Problem 6
  The directions "southwest" and "southeast" are orthogonal. Thus the described situation is a right triangle with legs <math>8</math>
  1 KB (154 words) - 19:23, 22 October 2022
• 1999 AHSME Problems/Problem 22
  Each of the graphs consists of two orthogonal half-lines. In the first graph both point downwards at a <math>45^\circ</ma
  3 KB (538 words) - 12:02, 17 October 2020
• 2009 AMC 12B Problems/Problem 22
  ...>B'=(s,0)</math>, <math>C'=(s+t,0)</math> and <math>D'=(t,0)</math> be the orthogonal projections of <math>B</math>, <math>C</math>, and <math>D</math> onto the
  6 KB (1,071 words) - 22:25, 9 October 2021
• 2009 AMC 10B Problems/Problem 22
  As the line <math>RN</math> is orthogonal to <math>QM</math>, it must have the equation <math>y+2x+q=0</math> for som ...r. This rotation will map the segment <math>MQ</math> to a segment that is orthogonal to <math>MQ</math>, contains <math>R</math> and contains the midpoint of <m
  12 KB (1,868 words) - 03:36, 30 September 2023
• 2011 AIME I Problems/Problem 13
  ...e <math>BD</math> makes a <math>2-14-10\sqrt{2}</math> right triangle, the orthogonal line makes the same right triangle rotated <math>90^\circ</math>. Therefore
  4 KB (613 words) - 11:37, 8 September 2022
• 2013 USAJMO Problems/Problem 5
  ...cyclic, and triangle <math>AXQ</math> is rectangle, and <math>CX</math> is orthogonal to <math>AZ</math>. Now
  7 KB (1,250 words) - 18:05, 1 October 2021
• 2014 AIME II Problems/Problem 14
  ...</math>. But <math>MO</math> and <math>AH</math> are parallel, both being orthogonal to <math>BC</math>. Therefore <math>MH:AO=MC:CO</math>, or <math>MH=\dfrac
  11 KB (1,442 words) - 19:28, 21 October 2023
• 1972 IMO Problems/Problem 6
  ...r of their <math>z</math>-coordinates. First take a plane <math>\pi</math> orthogonal to <math>\pi_i</math>, which cuts <math>\pi_1,\pi_2,\pi_3</math> along thre
  7 KB (1,370 words) - 15:42, 29 January 2021
• Asymptote: Crash Course
  So now that we've figured out exactly what the heck are perspective and orthogonal projection, let's find out how to do it in Asymptote.
  3 KB (410 words) - 20:22, 15 December 2020

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