1. The problem statement, all variables and given/known data 1) Find parametric equations for the line that is tangent to r(t) = (sin t)i + (t^2 - cos t)j + (e^t)k at the parameter value t = 0. 2) For the equation r(t) = (cos t)i + (sin t)j and for t >= 0, is the particle's acceleration vector always orthogonal to its velocity vector? 2. Relevant equations 3. The attempt at a solution 1) According to my text the tangent line to the curve r(t) = f(t)i + g(t)j + h(t)k is the line that passes through the point (f(t0), g(t0), h(t0)) parallel to v(t0), where t0 = 0 in this problem. I solved the velocity equation v(t) = (cos t)i + (2t + sin t)j + (e^t)k, and v(0) = i + k. This is the answer: x = t, y = -1, z = 1+t I found the point (f(0), g(0), t(0)) = (0, -1, 1), I'm not sure how to find the equation of a line that passes through this point and is parallel to another line? thanks 2) For this one I just want to make sure, to find where the acceleration vector is orthogonal to its velocity vector I find where their dot products equal 0, right?