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January 14th, 2010, 04:14 AM   #1
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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
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January 14th, 2010, 11:54 AM   #2
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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).
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