Suppose that a particle has position function () = ^2, t^2, t^3

Suppose that a particle has position function F(t) = (t3. t3. :3). A. Find the vector equation ofa line tangent to t) = (t2. t2. t3} at t = 1. B. Determine whether or not a line tangent to t) = (t2. t2. :3} at t = 1 will intersect the line through (2.2.2) in the direction {5 = {3. -2. -1}. Find the point ofintersection if it exists. C. Determine whether particles travelling along a line tangent to t) = (t2. t2. 3} at t = 1 and the line through (2, 2,5) in the direction is" = {3. 2, 1) would collide or would not collide if these lines intersect. D. If the speed of the particle is I]? |'(tr)|| = $18112 + 9H4, then, use calculus tond a function that represents how far the particle will travel along Ht) = (:2, t2, 3) for every t E El