The position vector r describes the path of an object moving in space. Find the velocity v(t), speed s(t), and acceleration a(t), of the object. r(t) = (3t, 4 cos(t), 4 sin(t)) V(t) = s(t) = a(t)The graph of the vector-valued function r(t) and a tangent vector to the graph at & = to are given. r(t) = (t, -+2, 1+3), to = 1 PA -2, (1, -1. 4) 2 (a) Find a set of parametric equations for the tangent line to the graph at t = to. (Enter your answers as a comma-separated list.) (b) Use the equations for the line to approximate r(to + 0.1). r(1 + 0.1) =Use the given acceleration function to find the velocity vector v(t), and position vectors r(t). Then find the position at time t = 3. a(t) = 5i + 4k v(0) = 7j, r(0) = 0 V(t) = r(@) - r(3) =