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Homework Help: Question from Lin Al quiz I'm pretty sure I got wrong.

  1. Oct 8, 2008 #1
    ok... back in school after a 3-week faculty strike.

    I'm pretty sure I got this wrong:

    specifics aren't important. the question was to find a point on a given plane closest to a point A.

    What I did was find a point B on the plane, and do proj(n)(AB)
    n being a normal to the plane.

    ... when I look in my textbook the answer to a question like this is perp(n)(BA). Are they both right, or did I do it wrong? ... I mean, it makes sense to me that a projection of AB onto n would land in the same place, no?
     
  2. jcsd
  3. Oct 8, 2008 #2

    Dick

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    I think so. Projecting onto the normal looks like what you want. I'm not sure what perp(n)(BA) means.
     
  4. Oct 8, 2008 #3
    I attached picture of what I drew on the exam.

    By perp, we use:

    perp(a)(b) = b - proj(a)(b)

    = b - (a dot b/a dot a)a


    The textbook uses that. I guess my question is is the perp(n)(BA) the same as the proj(a)(AB)
     

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  5. Oct 8, 2008 #4

    Dick

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    It looks like proj(a)(b) is the projection of b onto the direction of the vector a and perp(a)(b) is the component of b perpendicular to the direction of a. So proj(a)(b)+perp(a)(b)=b. I still think you did the right thing by projecting (AB) onto the normal.
     
  6. Oct 9, 2008 #5
    yea this is why I'm confused, because I too think it makes sense that it would be the projection onto the normal, but the book uses the perp.

    I dunno, I guess I'll have to wait till next thursday to find out. ugh. Honestly,, the faculty goes on strike for 3 weeks, now we have thanksgiving break/reading week... I don't know how I'm gonna make it with this class; the textbook is the worst I've ever seen, midterms are supposed to be at the end of this month, yet we've only had like two weeks of class. All I know is that according to the textbook I'm wrong, but I don't understand why.

    EDIT: okay, I figured out why it's wrong: I should be starting the projection at B, which is what the perp is, otherwise I'm just getting the distance between the two points. the sad part is that I actually did it right on the quiz the first time, then changed it. aghh. O well, live and learn.

    thanks :smile:
     
    Last edited: Oct 9, 2008
  7. Oct 9, 2008 #6

    Dick

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    Still think you did it right. The question asked for the distance from A to the plane, right? |proj(n)(AB)| is that thing. |perp(n)(AB)| is the distance from B to the point closest in the plane to A. Sorry to upset you, but unless you phrased the question wrong, you are still right.
     
  8. Oct 9, 2008 #7
    lol don't worry you can't upset me. I'm upset at teachers going on strike and me having to pay for a full semester plus living costs when I'm not getting a full semester's worth of education. ... and at myself for getting the question wrong. ... and at the laundry machine that took my quarters today and then blew a fuse and I had to pay twice. .... this has not been my month :rofl:

    And yea, it asked for the specific point on the plane, not the distance which is what I gave.
     
  9. Oct 9, 2008 #8

    Dick

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    Oh. Sorry then!
     
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