PART B K 5. Given * = (1, 4, -1), y = (1, 3, -2), and Z = (-2, 1, 0), determine a vector equivalent to each of the following: a. X - 2y - Z 1X - y + 32 C. X b. - 28 - 3y + 2 d. 3x + 5y + 32 6. Given p = 21 - j + k and q = -1 - j + k, determine the following in terms of the standard unit vectors. a. p + q b. p - q c. 2p - 5q d. -2p + 5q 7. If m = 21 - k and n = -27 + ] + 2k, calculate each of the following: a. m - n b. m + n c. 2m + 3n d. -5m 8. Given x + y = -i + 2j + 5k and x - y = 37 + 6j - 7k, determine x and y. C 9. Three vectors, OA = (a, b, 0), OB = (a, 0, c), and OC = (0, b, c), are given. a. In a sentence, describe what each vector represents. b. Write each of the given vectors using the standard unit vectors. c. Determine a formula for each of OA], |OB, and loc]. d. Determine AB. What does AB represent? 10. Given the points A(-2, -6, 3) and B(3, -4, 12), determine each of the following: a. OA C. AB e. BA b. OB d. AB f. BA 1 1. The vertices of quadrilateral ABCD are given as A(0, 3, 5), B(3, -1, 17), C(7, -3, 15), and D(4, 1, 3). Prove that ABCD is a parallelogram. 12. Given 2x + y - 22 = 0, x = (-1, b, c), y = (a, -2, c), and Z = (-a, 6, c), determine the value of the unknowns. A 13. A parallelepiped is determined by the vectors OA = (-2, 2, 5), OB = (0, 4, 1), and OC = (0, 5, -1). a. Draw a sketch of the parallelepiped formed by these vectors. b. Determine the coordinates of all of the vertices for the parallelepiped. T 14. Given the points A(-2, 1, 3) and B(4, -1, 3), determine the coordinates of the point on the x-axis that is equidistant from these two points.