Vector Questions Help

[BlueYoHo]

Ok tonight I decided to do vectors instead And of course, got stuck again:

A, B and C are points defined by position vectors , and 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 CM, but If I had AN and CM I could easily do that...

Thanks in advance

[TrueTears]

I suggest you do this for i)



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

to find ON just do OC + CN

If you are stuck still, free feel to ask and I shall post my working

[BlueYoHo]

Omg I hate when I do that. DUH I should have easily seen that, I'm gonna go work on it now, lol thanks.

[TrueTears]

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