Answer the following with reference to vectors.
a. (a) Define the position vector of a point in three–dimensional space.
b. (b) Explain the meaning of internal and external division of a directed line segment in vector terminology.
c. (c) A point R divides the segment joining two points A and B in the ratio m:n (internally). Give a convincing reason, without performing any numerical calculation, why the scalar coefficients that multiply the vectors a and b in the expression for OR must add up to 1.