the position vector of point A is 2i + 3j + k and the position vector of point B is 4i - 5j + 21k.

a.) (i) show that vector AB = 2i - 8j + 20k

(ii) find the unti vector u in the direction of vector AB

(iii) show that u is perpendicular to vector OA.

Let S be the midpoin=t of [AB]. THe line L1 passes through S and its parrallel to vector OA.

b.) (i) find the position vector of S.

(ii) Write down the equation of L1.

The line L2 has equation r = (5i + 10j +10k) + s(-2i + 5j -3k).

c.) explain why L1 and L2 are not parallel.

d.) the lines L1 and L2 intersect at the point P. Find the position vector of P.