Please solve all question with hand-written step by step

1. (14 points) Let rl(t) = (2t2 3t, 4c2t) and r2(t) = (5t, 3, Sint). Calculate thc following. (a) (2 points) Find (In. dt (Ir2 (b) (2 points) Find dt (c) (3 points) Find (rt(t) r2Ct)) dt (d) (3 points) Find the tangent vector at, the point rt (2). (e) (4 points) Find the parametrization of the tangent line at the point rl (2). 2. (13 points) Consider, in R3, the parallelogralll PQRS pictured here where P Q 1,2), and (1, 7, 8). S (a) (3 points) What are the coordinates of the point S? (b) (4 points) Using Fid, and thc point P, find an equation for the plane the parallelogram lies on. (c) (3 points) Calculate the area of the triangle PQR. (d) (3 points) Calculate thc area Of the, parallelogram PQRS.