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January 14th, 2010, 04:14 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, 11:54 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(A²+B²+C²)+(Ar+Bs+Ct+D) = 0 for u, and substitute that value into (r,s,t)+u(A,B,C). 

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distance, line, point 
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