Question

Linear Algebra: Question I-15: http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/part-a-vectors-determinants-and-planes/problem-set-1/MIT18_02SC_SupProb1.pdf Answer at: http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/part-a-vectors-determinants-and-planes/problem-set-1/MIT18_02SC_SupProbSol1.pdf In this question, how do we find dir QP?

Answer 1

I don't see an I-15...

Answer 2

oh you must mean I-5 ?

Answer 3

1I-5, p.10 i'm sorry

Answer 4

like it says, in the earlier exercise A-7 you can see (and should be able to prove) that a translation of a vector over 90deg corresponds to\[a\hat i+b\hat j\to b\hat i-a\hat j\]since\[\vec{QP}\perp\vec{OQ}\]then that implies that\[\text{dir}\vec{QP}=\cos\theta\hat i+\sin\theta\hat j\implies\text{dir}\vec{OQ}=\sin\theta\hat i-\cos\theta\hat j\]

Answer 5

@TuringTest this is only in the case that the vector is translated 90deg clockwise, right?

Answer 6

the only case? not sure I get the question...
there is no translation actually happening here, they are just showing you that given the direction of \(\vec{QP}\) you can relate to the direction of \(\vec{OQ}\) by what you learned in exercise A-7, which is needed to solve the problem

Answer 7

im sorry, but isn't it the direction of OQ that is more or less given here first, not QP?

Answer 8

@turingtest so we go from dirOP to dirQP and then
\[dir QP=\sin \theta i-\cos \theta i\]

Answer 9

yeah you are right, I just totally messed up earlier; I meant to tye\[\text{dir}\vec{OQ}=\cos\theta\hat i+\sin\theta\hat j\implies\text{dir}\vec{QP}=\sin\theta\hat i-\cos\theta\hat j\]

Answer 10

\[dir QP = \sin \theta i - \cos \theta j\]
i mean*

Answer 11

ok good :), then I understand!

Answer 12

yay :) it's been a while for me too, I guess I haven't forgotten too much.

Answer 13

@TuringTest , just to clarify my question earlier though, this "translation of a vector over 90deg ":

\[a\hat i+b\hat j\to b\hat i-a\hat j\]

should only work going counterclockwise then right?

Answer 14

hmm nevermind, guess this works both ways.

Answer 15

yes, I just double checked myself and came to the same conclusion: it works both ways

I really ought to take the whole OCW multi var course in detail :P

Answer 16

well, the french accent of Prof. Auroux makes it worthwhile almost by itself I'd say ;).

Just out of curiosity though, are you a math major in college or somewhat further on in life?

Answer 17

No, unfortunately I have been unlucky in my academic pursuits and am largely self-taught. I do intend to change that though. And why are you interested in OCW? Are you a student just trying to get ahead?

Answer 18

I'm taking these courses in preparation for grad school.
I had a liberal arts background in college, but trying my best to get into the field of economics, which requires quite a lot of math.

So this is my way of trying to make up for that knowledge gap.

Answer 19

Indeed. Well, I'm no economist, but I think that the education you can get from online resources like these is more than sufficient preparation for the field. I'm sure you'll do great :D
I'm off to do solid state chem, I just get distracted by interesting problems. Good luck!

Answer 20

thanks! good luck to you too!