The line AB is a common perpendicular to to two skew lines AP and BQ, and C and R are the midpoints of AB and PQ respectively. Prove by vector methods, that CR and AB are perpendicular.

I tried the vectors, AP=s, AB=b, BQ=c, and PQ=d

a.b=0, andb.c=0

CR=$\displaystyle \frac{1}{2}b+c-\frac{1}{2}d$

thenAB.CR=$\displaystyle b.(\frac{1}{2}b+c-\frac{1}{2}d)$

this would equal 0 ifb.dis equal to one but I don't see how that relationship comes about.

Thanks!