hi. i need answer on the questions below. please provide explanation or solutions if needed so i can better understand it. please also write the given in every item. thank you!

43. Use the definition of scalar product, d . b = ab cos #, and the fact that a . b = a,b, + a,b, + a,b, to cal- culate the angle between the two vectors given by a = 3.0i + 3.0j + 3.0k and b = 2.01 + 1.0j + 3.0k. A. 10 degrees B. 22 degrees C. 45 degrees D. 60 degrees E. No Answers 44. Two vectors A and B have precisely equal magnitudes. For the magnitude of A + B to be 100 times larger than the magnitude of A - B, what must be the angle between them? A. 1.0 deg B. 1.15 deg C. 2.24 deg D. 3.47 deg E. No Answers 45. Vectors A and B have equal magnitudes of 5.00. The sum of A and B is the vector 6.00j. Determine the angle between A and B. A. 38 deg B. 56 deg C. 83 deg D. 106 deg E. No Answers 46. A person going for a walk follows the path shown in Figure. The total trip consist of four straight-line paths. At the end of the walk, what is the person's resultant displacement measured from the staring point? Start 100 m End 300 m 200 m 30.09% 60.0 150 m A. 147 m at 43.00 deg S of W B. 276 m at 21.00 deg N of W C. 358 m at 2.00 deg S of E D. 453 m at 12.00 deg W of E E. No Answers 47. A man pushing a mop across a floor causes it to undergo two displacements. The first has a magnitude of 150 cm and makes an angle of 120" with the positive x axis. The resultant displacement has a magnitude of 140 cm and is directed at an angle of 35.0' to the positive x axis. Find the magnitude and direction of the second displacement. A. 59 m at 58 deg B. 85 m at 143 deg C. 163 m at 194 deg D. 240 m at 237 deg E. No Answers