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

[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?

 

[Dick]

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

 

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

 

[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.

 

[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 going to 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

 

[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.

 

[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

And yea, it asked for the specific point on the plane, not the distance which is what I gave.

 

[Dick]

And yea, it asked for the specific point on the plane, not the distance which is what I gave.

Oh. Sorry then!