This is not a project and/or assignment for marks, as theses are textbook questions, and will not be copying the tutors work/answers. Please answer all the questions in the space provided and in full details. Show ALL your steps and your calculations. Answer in complete sentences, with therefore statements, when needed. Take as much time as needed to answer all of the questions correct please and thank you. Will write a very neat and wonderful review afterwards.

Answer all questions in the space provided. Show ALL your steps in your calculations for full marks. Answer in complete sentences when necessary. 1. A parallelepiped is defined by vectors a = (2, -5, -1), b = (4, 0, 1), c = (3, -2, -2). What is the volume? 2. What is the magnitude of a projection p = (7,3) on q = (-4,2)? 3. Vectors u = (-3, b, 2) and v = (5, 2, 8) are given. The two vectors are orthogonal. What is the value of b? 4. A frictional braking force is applied at an angle on an object. The frictional braking force is 500N, and the angle it is applied at is 160. The object is moving forward through a displacement of 20m. Find the work done by the braking force to the nearest joule. IF1 = 500 N 160 Id = 20.0 mAnswer all questions in the space provided. Show ALL your steps in your calculations for full marks. Answer in complete sentences when necessary. 5. A force, IF|, of 20N is applied to a door with a width, |dl, in cm at 75, as shown in the given diagram. If the magnitude of the torque, (7|, is 18 N.m, what is the width of the door, Id] to the nearest centimetre? |FI = 20 N 750 6. What is the measure of the angle 0 between the vectors u = (6, 2, 1) and v = (-4, 1,2)? 7. Sara wants to show that (@ x b) x & # a x (b x c). Yasmina says that it is impossible and comes up with three sets of vectors to prove Sara wrong. Do any of Yasmina's sets of vectors prove Sara's statement to be correct? Explain with words and math. | i. a = (1, 0, 0), b = (0, 1, 0), c = (0, 0, 1) ii. a = (1, 1, 0), b = (1, -1, 0), c = (0,0, -1) iii. a = (1, 0, 0), b = (1, 1, 0), c = (1, 1, 1)