7. Given 3? = 2? —_,i and y" = —i + 5}, find a vector equivalent to each of the following: _. a. 33." — y b. —(:r' + 2;} + 3(—}' — 3;) c. 2(5? + 3}) — 36 + 533) 8. Using 3? and 5? given in question 7. determine each of the following: a.|5r'+}'| b.|3r'-S;l c. PIE—357] d. lily—2?] 9. a. For each of the vectors shown below, determine the components of the related position vector. b. Determine the magnitude of each vector. CHAPTER 6 325 10. P_ar'allelogram OBCA is determined by the vectors 0—K = (6. 3) and OB = (l l. —6). a. Determine 0—6", a. and 8—6". h. Verify that la'l = erC']. II. AABC has vertices at A(2. 3), 3(6, 6). and C(-4, II). a. Sketch and label each of the points on a graph. b. Calculate each of the lengths |A—B'|, AC , and IE]. c. Verify that triangle ABC is a right triangle. 12. A parallelogram has three of its vertices at A(— l, 2), 3(7. —2), and C(2, 8). a. Draw a grid and locate each of these points. b. On your grid. draw the three locations for a fourth point that would make a parallelogram with points A. B. and C. c. Determine all possible coordinates for the point described in part b. 13. Determine the value of .r and y in each of the following: a. 3(1. l) - 5(2. 3y) = (ll.33) b. —2(x..r + y) — 3(6.y) = (6,4) 14. Rectangle ABCD has vertices at A(2, 3). B(—6. 9). C(x. y). and 0(8, l l ). a. Draw a sketch of the points A, B, and D. and locate point C on your graph. b. Explain how you can determine the coordinates of point C. 15. A(5. 0) and 3(0. 2) are points on the x- and y—aJtes. respectively. a. Find the coordinates of point P(a, 0) on the x—axis such that IE4) = IP—B-l. b. Find the coordinates of a point on the y-axis such that |Q—B'l = |Q—A.l.