1. In the triangle OAB, let M, N and P be the midpoint of the sides OB, AB and OA respectively. Let the perpendicular bisectors of sides AB and OA meet at G as shown. Let the position vector of P and M be p and m respectively and let

be denoted by r as shown.

a) show that m = p + r
this i have done
b) Let

be detnoed by v and

be denoted by w, as shown. One possible expression for

is

= v - p + m = v+r, by a)
Use this expression to show that

. p = r . p
how do you do b)?
2. A radar tracking facility tracks a plane flying in a straight line. With the radar facility as the origin, the plane's initial and final position vectors are a = 2i + 8j + k and b = 8i -4j + 13k respectively.
a) Find a unit vector , u , in the direction of the motion of the plane.
this i found to be
)
b) The position vector of the plane, p, when it is closest to the radar can be expressed as p = a +

u, where

is a real number. find the value of

and hence the plane's position when it is closest to the radar facility.
Any help on b)? I've tried letting p = ai +bj +ck but that just gets too many equations and can't be solved.
thanks guys!