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help on method for distance from line to point (FP4) watch

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    ok i made this up so the numbers probebly wont come out nicely

    point A is (1,7,19)

    line L is r=(5,16,-12) + t(9,7,-4)

    (the (9,7,-4) is direction vector but i cant use latex thing sorry)

    find distance from the point to the line...

    please just run through the possible methods 1 so i can see if i did i right, and 2 to see which of the 2 i used i got wrong

    will tell u how i did it if u want but i probebly got it wrong both ways lol

    thanks ...
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    anyone?
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    Post your working.
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    method 1

    from equation of line, with parametre t=0
    => point B is (5,16,-12)

    AB = B-A = (4,9,-31)

    i used the scalar product of

    AB dot (9 7 -4) all over mod (9 7 -4)

    giving 223 over root 146

    approx 18.46
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    method 2

    point P is a general point on the line where a perpendicular to the line which also passes through the point A intesects the line

    AP = OP - OA = ( 9t+4 7t+9 -4t-31 )

    BP = t( 9 7 -4 )

    then if AP dot BP = 0 ... cos (angle between) = 0 so angle is 90 deg

    => ( 9t+4 7t+9 -4t-31 ) dot ( 9 7 -4 ) = 0

    => 146t + 223 = 0

    => t -223/146

    => mod AP = ( (9(-223/146)+4) (7(-223/146)+9) (-4(-223/146)-31) )

    => mod AP = 1/146(root 1423^2 + 247^2 + 3634^2 )

    => mod AP is approx 26.8

    thanks...
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    both need the sketch to understand properly but i cant upload one so any help appretiated im sure im just eplaining my problem poorly though lol
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    A correct method (I haven't looked at either of yours) would be to use the point 5,16,-12 on the line (call it B) and find the distance from it to A. This is AB.

    Now find the vector to A from B and the vector from B to another point on the line. Use the scalar product to find the angle.

    Now use sin(angle) = O/AB where O is the shortest distance.
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    definatly the second method. i got 26.8 when i did it my way

    yo do (modPAxPB)/modPB

    i j k
    9 7 -4 = -181i + 263j + 53k = AP
    4 9 -31

    (32761+69169+2809)=(104739)

    root of (104739) divided by root of (146) = 26.8


    BAM lol
 
 
 
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Updated: January 26, 2010
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