1條 會考amaths vector

C is a point on OA such that OC:CA=1:2 D is a point on OB such that OD:DB = 1:x
where x>0 P is a variable point on AD such that DP:PA=1:y where Y>1 let OAvector=a OBvector =b



(a) express CDin terms of x , a and b


(b) if CD is parallel to AB and C,P,B are collinear
(i)by using vector method find the value of x
(ii) express CB in terms of a and b
(ii) express CP in terms of y ,a and b
hence fing the value of y and CP:PB