Let the points A(1,2,3), B(5,0,7) and C(−1,4,2) be the vertices of a triangle.
a. (i) Find the unit vector along the median from A to side BC.
b. (ii) Determine the length of this median.
c. (iii) The point D divides the median from A to BC in the ratio 2:1 (measured from A). Using the unit vector found in part (i), find the coordinates of D.
d. (iv) Show that the centroid of triangle ABC lies two–thirds of the way from A towards D, confirming your result in part (iii).