Find a vector parametric equation r (t) for the line through the points P=(-2,5,

Question

Find a vector parametric equation r(t) for the line through the points P=(-2,5,3) and Q=(0,2,0) for each of the given conditions on the parameter t.

a.) if r(0) = <-2,5,3> and r(7) = <0,2,0>, then r(t) = ?

b.) if r(3) = P and r(7)=Q, then r(t) = ?

c.) If the points P and Q correspond to the parameter values t=0 and t=-3, respectively, then r(t) = ?

If you could show every steps. I really don't understand this and I tried looking at other similar problems but I don't understnad where some values are coming from.

b.)

Explanation / Answer

a) I know at t t=0 r=P and t=7 r=Q

PQ = <2,-3,-3>
     r(t) = <-2 + t(0+2)/7), 5 + t(2-5)/7, 3 +t(-3)/7>
     r(t) = <-2 + 2t/7, 5 - 3t/7, 3 - 3t/7>

b) r(3)=P and r(7)=Q

r(t) = <-2 + t(0+2)/4), 5 + t(2-5)/4, 3 +t(-3)/4>
     r(t) = <-2 + 2t/4, 5 - 3t/4, 3 - 3t/4>

c) t = 0 and t = -3

r(t) = <-2 + t(0+2)/-3), 5 + t(2-5)/-3, 3 +t(-3)/-3>
     r(t) = <-2 - 2t/3, 5 + t, 3 + t>

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