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

1. Oct 8, 2008

moe darklight

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. Oct 8, 2008

Dick

I think so. Projecting onto the normal looks like what you want. I'm not sure what perp(n)(BA) means.

3. Oct 8, 2008

moe darklight

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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4. Oct 8, 2008

Dick

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.

5. Oct 9, 2008

moe darklight

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

Last edited: Oct 9, 2008
6. Oct 9, 2008

Dick

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.

7. Oct 9, 2008

moe darklight

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.

8. Oct 9, 2008

Dick

Oh. Sorry then!