I want it to be very detailed please

Short Answer: Write the final simplified answer on the answer lines. [6] 1. Consider points A(1, 3, - 7) and B(0, 2,-4). a) What is the vector AB? b) What is the exact magnitude of AB? 2. Consider the vectors u = [4. 3] and v = [2,-5]. a) Evaluate u . v. b) Determine the angle between & and v. 3. Consider the vectors u = f+2f -5F and v = 31-4f. a) Determine ux v. b) Determine the area of a parallelogram defined by a and v. Long Answer: Provide fully justified and simplified solutions to each of the following questions. 4. Determine the projection of vector v, on vector u. Vector u=[8,3] and Vector v=[2,7] [3]5. Determine the force as a Cartesian vector. 125M applied upward [3] 6. Determine the work done by the force, [300,700,500] in newtons, for an object moving along the vector, 5, [11,12]. in metres. [3] i'. A force of 200M is applied to a wrench in a clockwise direction at 80 degrees to the handle, 10 cm from the centre of the bolt. Calculate the magnitude of the torque. [3]