Find the unit tangent vector T(t) and find a set of parametric equations for the line tangent to the space curve at point P. r(t) = (3 cost, 3 sin z, 3), P(2. V/2. 3) Part 1 of 5 The unit tangent vector T(t) at t is defined as follows: TO = NO r(t) = 0 First find the derivative of r(t). r'(t) = {-3 sin (#),3 cos(#),0) (-3 sin(t), 3 cos(t), 0) Part 2 of 5 Now find the magnitude of r'(t). | |r'(t)|) = / (-3 sin ()2 + (3 cos ()2 + (0)2 = \\ 9 sin t + 9 cost = 3 V PB Part 3 of 5 The unit tangent vector T(t) at t is as follows: T(t) = (-3 sin t, 3 cos t, 0) 3 = W/ H -3 sin(t),3 cos( t),0) (-3 sin(t), 3 cos(t), 0) Part 4 of 5 Verify that t = 1 at the point P( 71 17, 3). That is, evaluate r(). Find the unit tangent vector at t = . T(t) = 1( -3 sin t, 3 cost, 0) "(#) - 3- 3 sin(I). 3 cos(#). 0)Find v(t), a(t), T(t), and N(t) (if it exists) for an object moving along the path given by the vector-valued function r(t). (If an answer is undefined, enter UNDEFINED.) r(t) = 3ti - 3tj V(t) = a(t) = T(t) = N(t) = Use the results to determine the form of the path. O quadratic O hyperbolic O sinusoidal O straight line Is the speed of the object constant or changing? O constant O changing O can not be determined