Q.The points A, B and C have position vectors $\bar a,\bar b$ and $\bar c$ respectively. The point P is midpoint of AB. Find in terms of $\bar a,\bar b$ and $\bar c$ the vector $\overrightarrow{PC}$.

The position vector of a point P with respect to a fixed origin O is the vector OP itself; writing P as (x, y, z) gives OP = x i + y j + z k, and its magnitude sqrt(x^2+y^2+z^2) is the distance of P from the origin. If two points A and B have position vectors a and b, the vector joining them, from A to B, is AB = b - a; in coordinates, for A(x1,y1,z1) and B(x2,y2,z2), AB = (x2-x1) i + (y2-y1) j + (z2-z1) k, and its magnitude reproduces the usual distance formula between two points in space. This single idea -- that the vector from one point to another is simply (position vector of th …