Answer:
r(t)= (5,6,7) + (4,2,-5)*t
Step-by-step explanation:
one way to describe the line r is though parametric equations r(t), where
r(t)= P₀(x₀,y₀) + v(x₁,y₁)*t
where
P₀(x₀,y₀)= any point that lies on the line = P(5,6,7)
v= vector parallel to the line = Q(9,8,2) - P(5,6,7) = (4,2,-5)
then
r(t)= (5,6,7) + (4,2,-5)*t
to verify it:
if t=0 →r(0)=P(5,6,7)
if t=1 →r(1)= Q(9,8,2)
