Electronic Homework Vectors in the Plane Work the following problems and choose the correct answer. G G G G G G G G 1. Let u 4i 3 j and v i j . Find u 5v . G G A. 9i 2 j G G B. 9i 8 j G G C. 9i 2 j G G D. 5i 2 j G G E. 21i 14 j F. None of these 2. Express the vector with initial point (1,-1) and terminal point (4,2) as a linear combination of the standard unit vectors. G G A. 3i 3 j G G B. 5i j G G C. 3i 3 j G G D. 3i 3 j G G E. 3i 4 j F. None of these G G 3. Let u be the vector with initial point (2,0) and terminal point (3,2). Let v Gbe the G vector with initial point (2,2) and terminal point (0,1). Find the sum of these vectors: u v . A. 3,5 B. 5,3 C. 1,1 D. 1,1 E. 1, 1 F. None of these. 4. Find the magnitude of the vector with initial point (1,-1) and terminal point (4,2). A. B. 34 20 C. 3 2 D. 5 E. 22 F. None of these G 5. Let u A. B. G 1,1 and v G G 3, 4 . Find the magnitude of the vector u v . 13 2 5 C. 41 D. 41 E. 13 F. None of these G 6. Let u G 8, 6 . Find a unit vector that has the same direction as u . A. 1,0 B. C. D. E. 1 1 , 8 6 3 4 , 5 5 4 3 , 5 5 1 3 , 2 2 F. None of these. G G G 7. Let v 4i 4 j . Find the direction angle that this vector makes with the positive x-axis. A. B. C. D. E. F. 30 degrees. 180 degrees. 45 degrees. 90 degrees. 5 degrees. None of these G 8. Let u A. 4,8 . Find the direction angle that this vector makes with the positive x-axis. S 6 §1 · B. arctan ¨ ¸ ©2 ¹ C. arctan(2) D. arctan(4) §1 · E. arccos¨ ¸ ©4 ¹ F. None of these 9. Find a vector that has magnitude 4 and that has a direction angle of G G A. 4 2 i 4 2 j G G B. 2 2 i 2 2 j G G C. 4i 4 j G G D. 2 2 i 2 2 j G G E. 2 2 i 2 2 j F. None of these 3S . 4 G 10. Given that the vector u x, 2 has magnitude 4 and that its direction angle with the positive xaxis is acute, what is the value of x? A. B. C. D. E. F. 2 12 -12 2 3 2 3 None of these 11. 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. B. C. D. E. F. -5 5 3 5 5 3 -10 None of these G G G G G G G G 12. Let u 4i 3 j and v i 2j . Find the dot product: u v . A. B. C. D. E. F. -2 2 12 10 14 None of these G G G G G G 13. Let u  i 3j and v i 3j . Find the angle between these vectors. A. B. C. D. E. F. 30 degrees. 120 degrees. 90 degrees. 150 degrees. 60 degrees. None of these G G 14. Given that the angle between the vectors u 1, k and v k2  4, 3 is 900; find all possible values of k . A. B. C. D. E. F. 2, -2 -1, 4 1, -4 -1, -2 -1,2 None of these G G G 15. Let u  4i 12 j . Which of the following vectors is orthogonal to this vector? G G A. 4i 12 j G 1 G j B. i 4 G 1 G j C. 3i 4 G G D. 3i j G G E. 3i  j F. None of these