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1. The vectors a, b, and & are shown. a Using these three vectors, demonstrate that a + (b + c) = (a + b) + a. Name this property and explain how your answer shows this to be true. 2. A(-2, 3, -5) and B(6, 7, 3) are two points in R'. Determine each of the following: a. AB b. AB c. a unit vector in the direction of BA 3. The vectors x and y are each of length 3 units, i.e., x = y = 3. If x + y = V17, determine x - y. 4. a. If 3x - 2y = a and 5x - 3y = b, express the vectors x and y in terms of a and b. b. Solve for a, b, and c: (2, -1, c) + (a, b, 1) - 3(2, a, 4) = (-3, 1, 2c). 5. a. Explain why the vectors a = (-2, 3) and b = (3, -1) span R2. b. Determine the values of p and q in p(-2, 3) + q(3, -1) = (13, -9). 6. a. Show that the vector a = (1, 12, -29) can be written as a linear combination of b = (3, 1, 4) and c = (1, 2, -3). b. Determine whether r = (16, 1 1, -24) can be written as a linear combination of p = (-2, 3, 4) and q = (4, 1, -6). Explain the significance of your result geometrically. 7. x and y are vectors of magnitude 1 and 2, respectively, with an angle of 120 between them. Determine 3x + 2y and the direction of 3x + 2y