# Vector lines, ratio of vector lines

1. Oct 26, 2012

http://www.xtremepapers.com/papers/...S Level/Mathematics (9709)/9709_w09_qp_31.pdf1. The problem statement, all variables and given/known data
6i

2. Relevant equations
r=a+λb

3. 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 cant get the awnser.

2. Oct 26, 2012

### 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.

3. Oct 26, 2012