Calculus: Find the Parametric Equation for the Line through P(1,2,0) and Q(1,1,-1)

Find the parametric equation for the line through P(1,2,0) and Q(1,1,-1)

PQ is the directional vector of line L

d = PQ

Find d by subtracting P from Q

d = Q-P = (1,1,-1) – (1,2,0) = (0,-1,-1)

We know that the parametric form is (where O is the origin):

(x,y,z) = P + td = OP + tPQ = (1,2,0) + t(0,-1,-1)

Final: Parametric equations:
x = 1
y = 2 – t
z = -t