How would you solve these?

1. If a = (5, -5, 3), b = (1, 2, 3), determin proj = (a onto b). 2. If a = (2, 2k), b = (4, -k), are perpendicular, solve for k. 3. Suppose a box on a frictionless ramp is being pulled by a rope with a tension of 350 N making an angle of 50 to the horizontal ground. If the angle of incline of the ramp is 20, and the box is pulled 5 m, determine the amount of work done. Hint: Draw a diagram and use vectors to represent the situation. 4. Two math students erect a sun shade on the beach. The shade is 1.5 m tall, 2 m wide, and makes an angle of 60 with the ground. What is the area of shade that the students have to sit in at 12 noon (that is, what is the projection of the shade onto the ground)? (Assume the sun's rays are shining directly down). a -b 5. Show that projob =