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Vector Assignment Unit 6-7 1. Given parallelogram ABCD, M, N are midpoints of AB and CB respectively. Let AM = u , and BN = v. Express the following in terms of u and v. a) CD b) BC C) DA d) AN e) ND f) CA 2. Given a regular hexagon ABCDEF, prove that AB + AC + AD + AE + AF = 3AD. Hint: Let AB = x and AF = y and express all vectors in terms of x and y. 3. An object of mass 20 kg is hung by a 5 m long rope attached to the ceiling. The object is pulled 2 m horizontally by a horizontal force. a) Determine the magnitude of the horizontal force. b) Determine the tension in the rope. 4. If v makes an angle of 60 with the y-axis and an angle of 1350 with the z- axis, what angle does it make with the x-axis? 5. Given that the two vectors 8a-b and 4a+3b are perpendicular and that | a |= 2| bl, determine the angle between a and b. 6. Show that aob = 1 (la + b|2 - la - 512). 7. A 4 m long beam, with a mass of 5 kg (The mass of the beam can 650 be considered acting at a point in the middle of the beam) is used to support the following system. It is attached to the wall by a hinge that allows the beam to rotate. The sign has a mass of 20 kg. The system is in equilibrium at 20 to the horizontal. a. Use net torque = 0, to determine the tension in the cable. MATH 20 b. What is the contact force (magnitude & direction) in the hinge of the beam