Parallel vectors have the same magnitude but not necessarily the same direction. A two hearing is a directed compass measurement, beginning at north and rotating clockwise. To subtract a vector from a given vector, add the opposite vector to the given vector. The dot product of two vectors is a vector. The dot product of two vectors can only be determined when the vectors are in Cartesian form. The projection of a vector onto another vector is a scalar. A normal vector to a line is perpendicular to that line. Idenrpe the choice that best completes the statement or answers the question. 8. When simplified, +ZF+E[E3V +1713) equals a. Si? e. 255V+263 h. E+U+i :2]. 5+6? 9. A ship is sailing at 5 knots (nautical miles per hour) on a heading of Gil-l)". The wind is blowing at 4 knots from a bearing of 206. Find the speed {the magnitude of the resultant velocity} of the ship. a. 1.35 knots e. 8.86 knots h. 19.06 knots d. 7.12 knots It}. A vector joins the points M{3, 2) and NH), 4}. Find 'MNJ. a. 5 e. 4 h. 2.36 d. 3.61 11. A child in a field runs 2|] m on a hearing of 1120", then 31) n1 on a bearing of 096. Find the displacement of the child from her starting position. a. 51} n1 e. 36.66 In 13. 41.36111 d. 25m 12. Which vector is perpendicular to [m, n]? a. [m,n] e. [1, 1] 13. De, m] d. [n, m] 13. If a = [1, 0, 1] and b = [-1, -1, 1], find a xb. a. [1, -2, -1] C. b. 0 d. [-1, 0, 1] 14. Given the points A(1, 2, 3), B(5, 4, 3), and C(2, 1, 2), find AB . AC. a. C. 2 d. 6 15. A force of 30 N is applied to the handle of a wrench at 70 to the handle, 15 cm from the centre of the bolt. Determine the magnitude of the torque. a. 4.23 N.m C. 423 N.m b. 1.54 N.m d. 154 N.m 16. A line passes through the points M(0, 1) and N(1, 4). Find a vector equation of the line. a. [x, y] = [1, 3] + f[0, 1] C. [x, y] = [0, 1] + #[1, 4] b. [x, y] = [0, 1] + /[1, 3] d. [x, y] = [1, 3] + #[0, 1]Short Answer 17. Using two ropes. Marion and Michael pull Dwm in a sleigh. They act at 30 to each other. Marion pulls with a 200 N force and the resultant force is 42!} N. With what force is Michael pulling the sleigh? Problem 18. An airplane is heading 040\" with an airspeed of son tenth. A wind from the west causes it to have the course 045 . Find the resultant gromdspeed of the airplane and the speed of the wind. 19. A 501} N sign is supported by a cable that makes a 45 angle with the vertical wall and is held out from the wall by a rigid pole that is perpendicular to the wall. Determine the tension in the cable. 20. Two forces act on an object at an angle ofd\" to each other. the force has a magnitude of III} N and the other has a magnitude of Hi} N. Determine the resultant force. using Cartesian vectors (let the lD-N force vector lie along the positive .r-anis]. and state the magnitude ofthe resultant and its direction