Thread: Parallelogram vector problem

The parallelogram OABC has it vertices at O (origin) and points A, B and C with poisition vectors a,b and c respectively. The point P is the mid point of AB and the point Q is the midpoint of BC. The line CP meets the line OQ at the point R ( intersection of lines)

a) write down in terms of a and c, the position vectors b, p and q of the points B, P and Q respectively.

b) Show that every point on the line CP has a position vector x of the form;

x=(1-k)a + 1/2(1-k)c where k is any real number

c) Find thevalue of k in the above formula such that x is a scalar multiple of q

(a), at least, is pretty straight forward. Have you done nothing on this yourself? If you just draw a picture you should see immediately that b= a+ c, p= a+ (1/2), and q= (1/2)a+ c,

Yeah i've completed part (a) but part (b) has got me stumped! Any pointers would be fantastic! Thanks again.