Hello I need some help with these 6 questions. If you could please show me all your work on a separate sheet of paper with the solutions/answers that would be great!

1. a) If a = 7 N and b = 3 N and the angle between these two geometric vectors is 350, determine a . b . b) If a = 15 N and 5 = 10 N and the angle between these two geometric vectors is 660, determine a . b . c) If two algebraic vectors are given as a = (3,5) and b = (-1,2) , determine a . b d) If two algebraic vectors are given as a = (-2,11) and b = (-5,-7) , determine a . b 2. If a = (5, -5, 3), b = (1, 2, 3), determine proj (a onto b). " 3. If a = (2, 2k) and b = (4, -k), are perpendicular, solve for k. 4. Calculate the angle, to the nearest degree, between the two vectors a and b given that | a | = 1 . 16 1 = 5 and a . b = 3. 5. 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). 6. Two people erect a tarp on the beach so that some shade is provided to keep them out of the sunlight. . The tarp is square with dimensions 2m by 2m. The height of the tarp is 1.5 m tall above the ground at it's highest side. What is the area of shade that the students have to sit in at 12 noon (that is, what is the projection of the tarp onto the ground)? (Assume the sun's rays are shining directly down). Q6 Side View 2m 15 m /2 m shaded Arta S