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iScience

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i'm given some line and a point (not on that line), and i want to find a line that is perpendicular to given line and passes through the given point.

here is what i've tried so far. please tell me where i went wrong.

given line:

x=at+x

y=bt+y

z=ct+z

given point: P(P

my method is to use coordinate transformation basically. but apparently i've done it incorrectly.

<x

http://i.imgur.com/dFs5FvQ.png

i wanted to redefine my origin at the point P such that the vector traversing through parameter t would always originate from point P like so

http://i.imgur.com/fvvWpoq.png

(where my starting point on the line ((t=0) is r

so to redefine the starting/initial vector..

<x

and here's where i think i got it wrong; i figured the following would give me the line's vector component

<a,b,c> - (P

my idea was, when find the magnitude of the line's new equation, then take the derivative with respect to t, then set this equal to zero and this would yield the minimum distance from P to some point along the line. but i tried this and the math is not working out where did i go wrong?

here is what i've tried so far. please tell me where i went wrong.

given line:

x=at+x

_{0}y=bt+y

_{0}z=ct+z

_{0}given point: P(P

_{x},P_{y},P_{z})my method is to use coordinate transformation basically. but apparently i've done it incorrectly.

<x

_{0},y_{0},z_{0}> is the initial point if you will on the line; it is the initial vector we are starting from when @ t=0. but this vector is with respect to some origin. as shown in the picture here.http://i.imgur.com/dFs5FvQ.png

i wanted to redefine my origin at the point P such that the vector traversing through parameter t would always originate from point P like so

http://i.imgur.com/fvvWpoq.png

(where my starting point on the line ((t=0) is r

_{0})so to redefine the starting/initial vector..

<x

_{0},y_{0},z_{0}> - (P_{x},P_{y},P_{z}) would give me [itex]\vec{Pr }[/itex]_{0}and here's where i think i got it wrong; i figured the following would give me the line's vector component

<a,b,c> - (P

_{x},P_{y},P_{z})my idea was, when find the magnitude of the line's new equation, then take the derivative with respect to t, then set this equal to zero and this would yield the minimum distance from P to some point along the line. but i tried this and the math is not working out where did i go wrong?

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