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 February 11th, 2019, 01:49 PM #1 Senior Member   Joined: Jan 2017 From: Toronto Posts: 209 Thanks: 3 Projecting points on a line - 2D a = (1, 0) b = (1, 1) c = (0, 1) L: x + y = 4/3 $\displaystyle Proj_{L}(a) = ? \\ Proj_{L}(b) = ? \\ Proj_{L}(c) = ? \\$ 1. How do I express x + y = 4/3 in matrix form for projection matrix multiplication? 2. Is it possible to calculate the projection{a,b,c} on L with matrix multiplication? February 11th, 2019, 03:42 PM #2 Senior Member   Joined: Jan 2017 From: Toronto Posts: 209 Thanks: 3 Plain Old Algebra $\displaystyle A = (0, 1) \\ L: x + y = 4/3 \\ \perp(L) : x = y \\ Point~A~lies~on~ \perp(L) : ax + b = c, (0) + b = 1, b = 1 \\ L_{1}: x + 1 = y \\ The~intersection~point~between~L~and~L_{1}: x + 1 = 4/3 - x \\ The~intersection~point: (1/6, 7/6)$ $\displaystyle B = (1, 1) \\ Point~B~lies~on ~\perp(L): ax + b = c, (1) + b = 1, b = 0 \\ L_{2}: x = y \\ The~intersection~point~between~L~and~L_{2}: x = 4/3 - x \\ The~intersection~point: (2/3, 2/3)$ $\displaystyle C = (1, 0) \\ Point~C~lies~on ~\perp(L): ax + b = c, (1) + b = 1, b = -1 \\ L_{3}: x - 1 = y \\ The~intersection~point~between~L~and~L_{3}: x -1 = 4/3 - x \\ The~intersection~point: (7/6, 1/6)$ Case closed... Thanks from topsquark Last edited by zollen; February 11th, 2019 at 03:50 PM. February 11th, 2019, 03:52 PM #3 Senior Member   Joined: Jan 2017 From: Toronto Posts: 209 Thanks: 3 I was hoping I could have used projection matrix to solve this problem... Tags line, points, projecting Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post central4motion Calculus 1 April 1st, 2015 01:32 PM fran1942 Calculus 5 April 2nd, 2012 08:48 PM omorawr Linear Algebra 1 August 12th, 2011 05:57 AM cafegurl Algebra 2 April 29th, 2010 07:48 AM kallog Real Analysis 0 March 12th, 2010 06:39 PM

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