(Solved): Consider the following curve. x = sin(4t), y = -cos(4t), z = 8t Using the given parametric equations ...

Consider the following curve. x = sin(4t), y = -cos(4t), z = 8t Using the given parametric equations, give the corresponding vector equation r(t). r(t) = (sin (4t), - cos (4t),8t) Find r'(t) and Ir'(t). (4 cos (4t),4 sin (4t),8) |r'(t) = ?16 sin² (4t) + 16 cos² (4t) + 64 r'(t) = Find the equation of the normal plane of the given curve at the point (0, 1, 27). x-2z=-4? Now consider the osculating plane of the given curve at the point (0, 1, 2). Determine each of the following. cos (4t) sin(4t) 2 10 ?10 ?10 T(t) = T'(t) = |T'(t) = N(t) = 2?/27/3 7 X 9 (-sin (4t), cos (4t),0) X