Please solve the problems attached below:

. Express the vector with initial point (1,-1) and terminal point (4,2) as a linear combination of the standard unit vectors. 3? + 4} 3E+33 A. B. C. 534} D. 31153} E. 3_f+3:f F. None of these . Let 5:41:13} and 34}. Find {4+5i}. A. 9?+2}' B. 9+83 C. 9L2} D. 5242} E. 212414} F. None of these . Find the magnitude of the vector i = Si 2} F. None of these . Find the magnitude of the vector with initial point (1,-1) and terminal point (4,2). . Let it be the vector with initial point (2,0) and terminal point (3,2). Let I: be the vector with initial point (2,2) and terminal point (0,1). Find the sum of these vectors: ii+ B . F. None of these. . Let it = (1,1) and ii: (3,4) . Find the magnitude of the vector ii +13. A. 13 B. 41 C. M D. JE+5 E. E F . None of these 7. Let u = (6,8). Find a unit vector that has the same direction as u . A. (1,0) B. 6'8 C. 1 3 15'5 D. 3 4 5'5 E. 4 3 5 ' F. None of these. 8. Let u = (4,8). Find the direction angle that this vector makes with the positive x-axis. A. B. arccos C. arctan(2) D. arctan NI- E. arctan(4) F. None of these 9. Let v=-4i +4 j . Find the direction angle that this vector makes with the positive x-axis. A. 30 degrees. B. 90 degrees. C. 180 degrees. D. 45 degrees. E. 135 degrees. F. None of these3;: 10. Find a vector that has magnitude 4 and that has a direction angle of Y . A. 2J5 E+2J 3 B. 4J5 E+4J }' C. 2J5 E2JE }' D. 2J E+2J }' E. 4M4} F. None of these 11. Given that the vector ii = (x, 2) has magnitude 4 and that its direction angle with the positive x- axis is acute, what is the value of x? D. 12 E. -12 F. None of these 12. A vector has magnitude 10 and it has a direction angle of 1200 with the positive x-axis. Find the horizontal component of this vector. A. 5 B. 55 C. 5 D. 10 E 5@ F. None of these 13. Let i: (2,3) and G: (5,2>. Find the dot product: 115. A. 8 B. 16 C. 4 D. 10 E. 8 F. None of these 14. Let I; = 4i+33i and 3:2; 2} . Find the dot product: 11\".; 15. Let I; = i+ J5} and i) =_i.+\\/}. Find the angle between these vectors. A. 60 degrees. B. 90 degrees. C. 30 degrees. D. 120 degrees. E. 150 degrees. F. None of these 16. Let I; = 2E+ 2} and I: i+\\/} . Find the angle between these vectors. (Hint: Graph each.) A. 90 degrees. B. 75 degrees. C. 135 degrees. D. 120 degrees. E. 60 degrees. F. None of these 17. Let i = 2i+ 6}. Which of the following vectors is orthogonal to this vector? (Hint: Try each choice and see if the vector given is orthogonal to I: .) A. 475+3} B. 5+6} C. 256} D. 414} E. 31+} F. None of these 18. Given that the vectors u = (1, k) and v = (k2 -8, 2) are orthogonal; find all possible values of k . A. 2, -2 B. -4, -2 C. -4, 2 D. 4, -2 E. 0, 4 F. None of these