Hate to ask this, but I'm getting desperate.



Determine the value of a which minimizes the perpendicular distance from point C to a section of pipeline that passes through points A and B.

The solution is a=2.08 m.

This is from the chapter on moments, so I'm guessing we minimize the distance by minimizing the moments.

This is what I have so far:

A: (0,-2,3)
B: (8,5,-6)
C: (-1,8,a)

I'm taking vector AB to be the force vector.

F=<8,7,-9>=F(lamda)AB=1/13.9 <8,7,-9>

r=CA=<1,-1.2,3-a>

Thus the moment is (X designates cross product):
M=r X F



=1/13.9 ( (7a-10.2)i + (33-8a)j + 16.6k)

From this point, I'm stuck. I know that M=Fd=F*r*cos (theta).

The hint the instructor gave included finding the magnitute of M and setting it equal to d. But that leaves too many unknowns, M, |F|, and a. Any suggestions would be great.

Thanks


[This message has been edited by Aaron (edited June 12, 2004).]

My brain hurts just looking at that.

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The Massassi-Map
There is no spoon.

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Welcome to my world.



[This message has been edited by Aaron (edited June 12, 2004).]

what the hell would ythe average person use something like that for?



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Old aunts used to come up to me at weddings, poking me in the ribs and cackling, telling me, "You're next." They stopped after I started doing the same thing to them at funerals.

WTF is that? Calculus?
if yes, then whoopie! Do I have one heck of a school year ahead of me

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nytfyre m0d || f33l t3h p0w3r || t3h l0st c0gz || OMF > *

Nah, its called engineering statics, which is basically like physics expect you only look at an instant in time, so basically nothing ever moves. Though I'm an engineering major, I see no reason for this class, I could understand for mech-es and civ-es, but not me (tentatively a chem-e). As for calculus, I've thought about using it, it might be easier. Simple linear optimization or maybe LaGrange multipliers. But I won't get full credit if I did it one of those ways, cause that's not what the concepts are. Calc II is a prerequiste, but I have yet to use it.

Anybody with a suggestion?

[This message has been edited by Aaron (edited June 12, 2004).]

It's simple, the answere is *snipe*

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-Proud Leader of the Minnessassian Council
<]-[ellequin> Nothing is quite as satisfying as placing a .177 lead pellet in between the eyes of a cat.
<]-[ellequin> I think I will leave it's corpse there, to warn all the other cats to keep out of my hibiscus patch

Live on, Adam.

Ok, got it.

First off, Aaron made a stupid mistake.

r=CA=<1,-1.2,3-a> is not right, I subtracted wrong, it should be:
r=CA=<1,-2.8,3-a>

Then what you have to do, is find the magnitude of M (w/ or w/o the 1/13.9), in this case: (113a^2-469.2a+1971)^.5, and find the value of a, which minimizes the value of d, in this case, a=2.0761062, which I determined graphically. So now I just got to do the work to show how to find it by hand (no big deal, just another step), so thanks for all the help guys

See, I knew that. Just the sniper who's name is *snipe*

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-Proud Leader of the Minnessassian Council
<]-[ellequin> Nothing is quite as satisfying as placing a .177 lead pellet in between the eyes of a cat.
<]-[ellequin> I think I will leave it's corpse there, to warn all the other cats to keep out of my hibiscus patch

Live on, Adam.