Chapter 1 Euclidean spaces 5. d = and 6 = Find all x , y E R such that d = b . 6. a - 24) and B - (x4 ). Find all x, y E R such that a - b is a nonzero vector. 7. Let P(1, x2), Q(3, 4), P, (4, 5), and Q, (6, 1). Find all possible values of x E R such that PQ = P Q1. 8. A company with 553 employees lists each employee's salary as a component of a vector a in R $53. If a 6% salary increase has been approved, find the vector involving a that gives all the new salaries. 110 9. Let d = denote the current prices of three items at a store. Suppose that the store announces a sale so that the price of each item is reduced by 20%. a. Find a 3-vector that gives the price changes for the three items. b. Find a 3-vector that gives the new prices of the three items. a E R. Compute i. 2d - b + 5c; ii. 4a + ab - 2c