Finding the Ratio of a Vector Division: Vector Equation Help

[Firepanda]

http://img404.imageshack.us/img404/5186/vectornw4.jpg

'Write Down the vector AM and hence the coords of the point N which divides AM so that the ratio AN:NM = 2:1.'

I know that ON = OA + AN

And that the vecor equation is

r = (0,0,6) + x(0,-4,-6)

But the answer is 9/13 for x, which i don't understand. I thought it would be 2/3 or 2/3 of the length AM. I am really stuck.

Thanks

 

[Dick]

Just take (r-A)^2=2^2*(r-M)^2 and solve for x. Or just notice x=0 gives A and x=1 gives M so the x that splits it 2:1 must be 2/3.

 

[Firepanda]

so ur saying x = 2/3?

thats what i said, but the answer says its 9/13 which i don't understand.

 

[Dick]

so ur saying x = 2/3?

thats what i said, but the answer says its 9/13 which i don't understand.

If I'm understanding the question, yes, I say x=2/3.