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 January 14th, 2010, 03:14 AM #1 Newbie   Joined: Jan 2010 Posts: 1 Thanks: 0 Distance between a point and a line Hi, I am using the formula: dist = |Ar+Bs+Ct +D| / sqrt(A^2 + B^2 + C^2) to find the distance between a point and a line for the line: Ax + By + Cz + D =0 and the Point: (r, s, t) Now that I have solved for the distance however, I would like to know which point on the line is closest to (r, s, t) How would I go about this? Thanks for any assistance January 14th, 2010, 10:54 AM #2 Senior Member   Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3 Re: Distance between a point and a line Ax + By + Cz + D = 0 is a plane, not a line. Its normal is the vector (A,B,C). So you need to find where the line (r,s,t)+u(A,B,C) intersects Ax + By + Cz + D = 0. Solve u(A�+B�+C�)+(Ar+Bs+Ct+D) = 0 for u, and substitute that value into (r,s,t)+u(A,B,C). Tags distance, line, point 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 abcdefgh123 Algebra 2 January 4th, 2014 03:08 PM BattalGazi Algebra 16 March 30th, 2012 03:21 AM arnav.akash9 Algebra 1 November 16th, 2009 11:27 PM greg1313 Algebra 2 November 5th, 2008 01:58 PM BattalGazi Linear Algebra 1 December 31st, 1969 04:00 PM

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