Consider the vector equation x = p + t(q - p), where p and q correspond to distinct poin...

Consider the vector equation x = p + t(q - p), where p and q correspond to distinct points P and Q in

(a) Show that this equation describes the line segment as t varies from 0 to 1.

(b) For which value of t is x the midpoint of , and what is x in this case?

(c) Find the midpoint of when P = (2, -3) and Q = (0, 1).

(d) Find the midpoint of when P = (1, 0, 1) and Q = (4, 1, -2).

(e) Find the two points that divide in part (c) into three equal parts.

(f) Find the two points that divide in part (d) into three equal parts.