Please work all 15 problems clearly and legibly. Thank you so much

1. Find the component form of the vector: the sum of vector AB and vector CD where A = (1,-1), B = (2,0), C = (-1,3) and D = (-2,2) 2. A kite string exerts a 12-lb pull on a kite and makes a 45 degree angle with the horizontal. Find the horizontal and vertical components of F. 3. For the vectors u = 10i + 1 1j - 2k and v = 3j + 4k find (a) uv, ul , v (b) The the angle between u and v (c) The scalar component of u in the direction of v (d) The vector projvul 4. How much work does it take to slide a crate 20 m along a loading dock by pulling on it with a 200 N force at an angle of 30 degrees from the horizontal? 5. Find the area of the triangle determined by the points P, Q, and R. P(2,-2, 1), Q(3,-1,2), R(3,-1,1). Also find the equation of the plane represented by the triangle. 6. Find parametric equations for the line through the point (3,-2,1) and parallel to the line x = 1 + 2t, y = 2 -t, z= 3t. 7. Find the magnitude of the torque generated by force F = 30 lb. applied to a bar 4 ft. long at an angle of 60. 8. Find the distance from the point (3,-1,2) to the line x = 2 + 2t, y = 1 + 6t, Z = 3. 9. Find the distance from the point (-1,1,2) to the plane 2x + y + 2z -4. 10. An athlete puts a 16 lb shot at an angle of 45 to the horizontal from 6 ft above the ground at an initial speed of 40 fu/sec. How long after launch and how far from the inner edge of the stopboard does the shot land? 11. Find the maximum height, flight time, and range of a projectile fired form the origin over horizontal ground at an initial speed of 55 m/sec and a launch angle of 60. 12. A golf ball leaves the ground at a 450 angle at a speed of 90ft/sec. Will it clear the top of a 30 ft tree that is in the way 235 ft down the fairway? Explain. 13. Find the angle between the planes 2x + 2y -z - 3 and x + 2y + z = 2 14. Find the point where the line x = 1 + 2t, y = 1 + 5t, z - 3t intersects the plane x ty +z=2 15. Find the length of the indicated portion of the curve. r(t) = (2 +t)i-(t+1)j+tk, Ost