Part 1:

Compute the partial derivatives of each function with respect to r and y. 1. f(x, y) = 2x3y2 - 2. g(x, y) = sin(xy?)1. Let = 27- 3j+ k and w =i+23 -k. Compute d x w. 2. Find an equation for the plane through the points (3, 4, 2), (-2, 1, 0), and (0, 2, 1). 3. Find the volume of the parallelepiped with edges a = -i + j + k, b = 1- j+ k, and c= 7+j- E. 4. Find a vector parallel to the line of intersection of the planes given by the equations 2x - 3y + 5z = 2 and 4x +y - 3z = 7. 5. Find an equation of the plane through the point (4,5, 6) and perpendicular to the line of intersection of the planes in Problem 4. 6. Given the points P = (1, 2,3), Q = (3,5, 7), and R = (2,5,3), find: (a) A unit vector perpendicular to the plane containing P, Q, and R. (b) The angle between PQ and PR. (c) The area of the triangle PQR. (d) The distance from R to the line through P and