Question

Please help...

Answer 1

The points O, A, B and C are such that OA = 6u−4v, OB= 3u−v and OC =v−3u, where u and v are non-parallel vectors.The point M is the mid-point of OA and the point N is the point on AB such that AN ; NB= 1 : 2a
Find
I)OM and ON?.
ii)Prove that C, M and N are collinear...

Answer 2

NO DIAGRAM

Answer 3

How are you supposed to do this without a diagram? :O

Answer 4

you can, they have expressed the values all u do is, using the values find the vector, i just did it but the : collinear C,M,N part, i did not get o.O

Answer 5

What were your answers to (i) ?

Answer 6

OM :3u-2v

Answer 7

ON : 5U-5V

Answer 8

shall i show the working, so that u can make sure i am right?

Answer 9

or wrong!

Answer 10

Yep!

Answer 11

OM : 1/2(OA)
= 1/2(6U-4V)
=3U-2V

Answer 12

That is correct!

Answer 13

ON= OA + AN
= OA + 1/3(AB)------> lets find: AB =AO + OB
AB =AO + OB
= -(6U-4V) + 3U-V
=-6U+4V+3U-V
-3U+3V

NOW---> OA + 1/3(AB)
= 6U-4V +1/3(-3U+3V)
= 6U-4V-1U-1V
=5U+5V

Answer 14

5U-5V* THE LAST PART

Answer 15

How can you cancel out 3 with (-3U + 3V) ? Shouldn't it be like (-3U+3V)/3?

Answer 16

it is possible right? o.O, the magnitude can be cancelled anyway

Answer 17

I got 5U-3V as the answer. O.o

Answer 18

how?

Answer 19

Ok, sorry! I forgot to put a negative sign. Your answer is correct.

Answer 20

okay now, u have to help me in the collinear thing...CAN U RIGHT IT IN A FORM LIKE
FOR EXAMPLE
AB= x.BC ?
how should i write?

Answer 21

I redid it. I don't why there is so much confusion. I'm still getting 5u-3v. Why don't you try it again?

Answer 22

yes okay, sorry...next?

Answer 23

As for the last part,
I think you should first find CM.
CM=OM-OC
=3U-2V-(V-3U)
=6U-3V

Now find MN.
MN=ON-OM
=5U-3V-(3U-2V)
=2U-V

CM=kMN
6U-3V=k(2U-V)
6U-3V=2kU-kV;

Equating 6U=2kU
k=3

Thus, CM=3MN.
CM/MN=3/1.
Hence they are collinear.

Answer 24

isnt is CN = k.CM

Answer 25

You can express it either way you want. Try with this one and see if you get the same answer.

Answer 26

what about k.CN= CM?

Answer 27

For this, you would get an anSwer in fractional form. Since, CN is bigger than CM.

Answer 28

so always the small one multiply by the constant = bigger one
right?

Answer 29

well i am getting a fraction for the CN = k.CM? so the constant does change o.O?

Answer 30

@thushananth01 : What fraction did you get? If possible, show your working here.