Recall that an ellipse centered at the origin with major axis of length 2a and minor axis of length 2b, where a > b, may be represented by the equation + 12 = 1. Note that the vector equation r(t) = (a cos(t), b sin(t), 0), te R parameterizes this ellipse as a 3D space curve in the xy - plane (see below). For the remainder of the problem use the version of T (t) that parameterizes the ellipse with equation + =1 1. (8 points) Give a non-zero vector orthogonal to both T' (7/2) and " (7/2). 2. (4 points) Determine the curvature K(7/2) of the ellipse at t = 1/2. 3. (4 points) If a particle moves along the ellipse according to T (t), determine the normal component an of its acceleration at time t = 1/2. (Hint: Recall aN = KU=). 4. (4 points) Write down (DO NOT SOLVE) a definite integral describing the distance traveled by a particle that traverses the ellipse exactly once. (Hint: Recall that the unit circle has parameterization (cos(0), sin(0)) and is traced exactly once as 0 rotates through 27 radians.)