Calculus parametric

Question

A particle moves at a constant speed along a line through P=(1,−1,9) to point Q=(−3,−1,−4). Find the parametric equations for its potions at time t if the particle passes through P at time t=2 and through point Q at time t=8. What is x(t) y(t) z(t)

Answer 1

r(t) = <1,-1, 9> + (t - 2)·PQ/(8 - 2) = <1, - 1, 9> + (t - 2)·<- 3 - 1, - 1 + 1, - 4 - 9>/6 =

<1, - 1, 9> + (t - 2)·< - 4, 0 , - 13>/6 = <7/3, - 1, 40/3> + t·<- 2/3, 0, - 13/6>

x(t) = 7/3 - 2t/3

y(t) = -1

z(t) = 40/3 - 13t/6