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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: BlueYoHo on March 16, 2009, 10:12:33 pm

Title: Vector Questions Help
Post by: BlueYoHo on March 16, 2009, 10:12:33 pm: Ok tonight I decided to do vectors instead :P And of course, got stuck again:

A, B and C are points defined by position vectors $2i - j - 4k$ , $-i + j + 2k$ and $i - 3j - 2k$ respectively.
M is a point of line segment AB, such that |AM| = |AC|.

Find:
i) AM
ii) the position vector which represents N, the midpoint of CM.

And the last part is hence show AN $\bot$ CM, but If I had AN and CM I could easily do that...

Thanks in advance :)
Title: Re: Vector Questions Help
Post by: TrueTears on March 16, 2009, 10:15:23 pm: I suggest you do this for i)

$AM= kAB k \in R$

Now, find AB = OB - OA

then find AC = OC - OA

AM = k(OB - OA)

so |AM| = | AC| Find the magnitude of AM in terms of k and magnitude of AC. Then solve for k :)

then sub k back in AM = k(OB-OA) and find AM

for ii) after you get k and found AM you can find OM which is just OA + AM.

Now that you have OM ( the position vector of M) you can find CM which is OM - OC, then CN must be $\frac{1}{2}(OM - OC)$

to find ON just do OC + CN

If you are stuck still, free feel to ask and I shall post my working :)
Title: Re: Vector Questions Help
Post by: BlueYoHo on March 16, 2009, 10:20:49 pm: Omg I hate when I do that. DUH I should have easily seen that, I'm gonna go work on it now, lol thanks.
Title: Re: Vector Questions Help
Post by: TrueTears on March 16, 2009, 10:24:26 pm: Quote from: BlueYoHo on March 16, 2009, 10:20:49 pm
Omg I hate when I do that. DUH I should have easily seen that, I'm gonna go work on it now, lol thanks.
Hehe, those questions get trivial after some good vectors grinding :)