Consider the vector equation x=p+t(q-p) where p and q correspond todistinct poin

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Consider the vector equation x=p+t(q-p) where p and q correspond todistinct points in R2 or R3.

(a) Show that this equation describes the line segment PQ as tvaries from 0 to 1.
(b) For which value of t is x the midpoint of PQ and what is the xin this case>
(c) Find the midpoint of PQ when P=(2,-3) and Q=(0,1)
(d) Find the midpoint of PQ when P=(1,0,1) and Q=(4,1,-2)
(e) Find the two points that divide PQ in part (c) into three equalparts.
(f) Find the two points that divide PQ in part (d) into three equalparts.

Any help is appreciation--much thanks in advance.

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