1. The problem statement, all variables and given/known data I was given parametric equations. x(t) = a(t) y(t) = b(t) z(t) = c(t) where a, b, and c are functions that depend on t. I was supposed to find equation of the tangent line at t = f given: x(f)= m y(f) = n z (f) = o where m,n,o are some constant numbers and given x'(f)=y'(f)=z'(f)= 0 2. Relevant equations I think this is the relevant equation though its not given. r(t) = <Px,Py,Pz>+tv 3. The attempt at a solution I'm super confused here. Given that the derivative of x(t),y(t),z(t) are all 0 at t=f. Then There is no slope whatsoever. That means its basically 3 intersecting planes where x=m, y=n, and z=o. Which isn't a line but a point. If I use the equation for a line r(t) = <Px,Py,Pz>+tv then, <Px,Py,Pz> = <m,n,o> and v = <0,0,0> so r(t) = <m,n,o>+t<0,0,0> = <m,n,o> But <m,n,o> is a vector with direction, while I already know that the tangent is only a point (m,n,o) given by the intersection of planes x=m, y=n, z=o. Is <m,n,o> vector really the tangent line, I feel like there is no 'line' as its a point.