Need help with math practice

Hi everyone...

I'm currently taking CIE a level maths, and tomorrow I'm going to have a test about vectors. Sadly, I can't do the question below (and so does most of the questions about vectors), so can someone explain how to do the question below? (The question is copied directly from the xtremepapers.)

7. With respect to the origin O, the position vectors of two points A and B are given by −−→OA = i + 2j + 2k and −−→OB = 3i + 4j. The point P lies on the line through A and B, and −−→AP = λ−−→AB.
(i) Show that −−→OP = (1 + 2λ)i + (2 + 2λ)j + (2 − 2λ)k. [2]
(ii) By equating expressions for cosAOP and cos BOP in terms of λ, find the value of λ for which
OP bisects the angle AOB. [5]
(iii) When λ has this value, verify that AP : PB = OA : OB. [1]

Note: For ii, I have attempted the question by using the cos formulae for the cos AOP and BOP; now what should I do next?