Some Core 4 Questions

Hello, I have a question that I can do, but I'm not at all sure if I'm doing it right.

2a) The points A and B have position vectors a and b, and P is the point which divides them in the ratio lamda :frown:

1-lamda). Show that the position vector of P is (1-lamda)a + lamda b - how do you show this (it's worth three marks)?
b) The vertices A, B and C of a triangle have non-coplanar position vectors a, b and c. The points D and E lie on AB and AC such that AD :biggrin:

B = 1:2 and AE :colone:

C = 1:2. The lines BE and CD intersect at F. Find the position vector of F ??

Any input appreciated!

Any takers?

Well firstly AB= b - a
(b and a are vectors but i wont bother bolding them)
call lambda x

now, AP = (b-a)x since this is the ratio of the line joining AB that goes up to P.
from the origin A= a, so P position is a+ (b-a)x. collect terms and you get your answer.

Reply 3

silent ninja

part (b) is messy, i hate those questions. I get 0.5a + 0.25b + 0.25c ?
It may be wrong because these q's are messy and i did it quickly. If its right i can post up.