Answer Happy

Suppose that a particle has position function r(t) = (t², t², t³). A. Find the vector equation of a line tangent to r(t) = (t², t², t³) at t = 1. B. Determine whether or not a line tangent to r(t) = (t², t², t³) at t = 1 will intersect the line through (2,2,3) in the direction = (3,-2,-1). Find the point of intersection if it exists. C. Determine whether particles travelling along a line tangent to r(t) = (t², t², t³) at t = 1 and the line through (2,2,2) in the direction v = (3,−2,−1) would collide or would not collide if these lines intersect. D. If the speed of the particle is || '(u)|| = √8u² + 9u4, then, use calculus to find a function that represents how far the particle will travel along r(t) = (t2², t², t³) for every t > 0.