Vector lines, ratio of vector lines

[thoradicus]

http://www.xtremepapers.com/papers/CIE/Cambridge%20International%20A%20and%20AS%20Level/Mathematics%20%289709%29/9709_w09_qp_31.pdf

Homework Statement

6i

Homework Equations

r=a+λb

The Attempt at a Solution

first i find AB which is (2,2,-2)
the equation if line is then (1,0,-1)+λ(2,2,-2)
i made it so that λ is 0.5, which then OM is (2,1,-2), as its the mid point.

i found AC to be (3,-3,3)

the equation of AC is (1,0,-1)+λ(3,-3,3)
which then i made lambda to be 1/3...but is this the right working? i did that and i can't get the awnser.

 

[HallsofIvy]

N is 2/3 of the way from A to C so is closer to C than A. Take $\lambda= 2/3$, not 1/3.

 

[thoradicus]

gah, didnt notice that. I am such an idiot >< thanks a lot.