\f23. Given v4 = 7i - 3j and vs = -i + 4j. Simplify the following. -VA + 4V5 D a. (-11, 19) D b. (11, -19) D c. (-11, -19) D d. (11, 19) Topic covered in 9.6 | Report a problem 24. Given v = (2,5) and w = (-5, -1). Find and express v + was a linear combination of the standard unit vectors. Then find the magnitude of v + w. D a. -3i + 4j, lv + wil = vi D b. -3i + 4j, llv + wil = 5 D c. 71 + 6j, |/v + w| = v13 D d. 7i + 6j. |v + wll = v85 Topic covered in 9.6 |~ Report a problem 25. Find the unit vector that points in the same direction as the following vector. V = (0, 4) D a. (1, 0) D b. (0, 1) D c. (-1, 0) D d. (0, -1) Topic covered in 9.6 | Report a problem30. Given v1 = (1, -1) , v2 = (-3,2) , and v: = 3 Simplify the following. 3v1 - 4v2 + 8v3 a. -19. 41 3 D b.(19, 41 c. (-19, d. ( 19, 41 Topic covered in 9.6 | Report a problem 31. Find the vector v in component form given its magnitude and direction angle. Ivil = 4, 0 = 150% O a. (-2V/3, -2) O b. ( -2V/3, 2) c. (2V/3, -2) d. (2V/3, 2) Topic covered in 9.7 | Report a problem32. Find the vector v in component form given its magnitude and direction angle. |vl = 1, 0 = 2100 O a, O b. /3 2 O /3 C O d. 2 Topic covered in 9.7 | Report a problem 33. Find the vector v in component form given its magnitude and direction angle. |vil = 4, 0 = 240% D a. (-2, -2V/3) b. ( -2, 2v3) D c. (2, -2V/3) d. (2,2v/3 Topic covered in 9.7 | Report a problem\f37. Find the angle between the two given vectors. v = -2i + 7j, w = (3,5) D a. 0.800 D b. 0.700 D C. 45.860 D d. 10.070 Topic covered in 9.7 |~ Report a problem 38. A ship is heading $ 100 E at 40 miles per hour. A current is moving $ 150 W at 10 miles per hour. Find the ship's velocity vector representing its true heading. D a. (-4.36, -49.05) b. (-4.36, 49.05) D c. (4.36, -49.05) D d. (4.36, 49.05) Topic covered in 9.7 |" Report a problem 39. Find the angle between the two given vectors. v = (3,9) , w =i -3j D a. 143.130 D b. 1800 D c. 2.500 D d. 0.800 Topic covered in 9.7 | Report a problem3. Find the polar coordinates of the point with the given rectangular coordinates. (3, 3) D a. (-3v/2, -4) b. (3V/2, D C. (3V2, = ) > d. ( - 3v2 , # ) Topic covered in 9.5 | Report a problem 4. State the quadrant in which the following point (given in polar coordinates) is located. -4, Da. I b. II D C. III Od. IV Topic covered in 9.5 | Report a problem5. State the quadrant in which the following point (given in polar coordinates) is located. 5. 3 Da. I O b. II D C. III Od. IV Topic covered in 9.5 |~ Report a problem 6. Transform the given point from its polar coordinate form into its rectangular coordinate form. 2, a. (v2, v2) b. (v2, -v2) D c. (-V2 -V2) D d. (-v2. v2) Topic covered in 9.5 |~ Report a problem3'. Which of the choices is another representation of the given point in polar coordinates? (49 9999 ml:- Topic covered in 9.5 F Report a problem 8. State the quadrant in which the following point {given in polar coordinates) is located. {-4, -159) CD a.[ CD b.[I CD c. III CD d.N 9. Which of the choices is another polar coordinate representation of the given point? (4, 3150) D a. (4, 450) b. (-4, 3150 ) D c. (-4, 1350 ) d. (4, 1350) Topic covered in 9.5 |~ Report a problem 10. Transform the given polar equation to an equation in x and y. a. y = x D b. y = - x D cy= x+1 D d. y = x - 1 Topic covered in 9.5 |~ Report a problem 11. Transform the given polar equation to an equation in x and y. r = 3 sec 8 O a. x = 3 b. x = - 3 D cy = 3 D d. y = - 317. Sketch the following vector in standard position. State the quadrant in which it lies. (-7: -2) Da. I D b. II D c. III D d. IV Topic covered in 9.6 |~ Report a problem 18. Find the vector Po in component form (a, b) , where the coordinates of P and Q are given. P(1, 2), Q(3, 4) D a. (-2, -2) D b. (-2, 2 ) D c. (2, -2) D d. (2, 2) Topic covered in 9.6 |~ Report a problem 19. Find the vector po in component form (a, b) , where the coordinates of P and Q are given. P(-2, -3), Q(4, 5) a. (-6, -8) b. (-6, 8) D c. (6, -8) D d. (6, 8)