7/31/23, 2:31 AM Vectors Assignment Vectors Assignment 1. What is the difference between a vector and a scalar quantity? [2 marks] 2. Classify each measurement as a vector or a scalar. [3 marks] a. The volume of a bottle is 591 ml b. A car is travelling at 85 km/h c. proj v d. A ship is sailing at 45 knots with a bearing of 172 e. AB f. The moon's phases cycle every 29.5 days. 3. Write each true bearing as an equivalent quadrant bearing. [4 marks] a. 12 b. 98 c. 225 d. 271' 4. Write each quadrant bearing as an equivalent true bearing. [2 marks] a. S12W b. N50 W 5. Use geometric addition of vectors to find the resultant of each combination. a. 18 km/h north and 16 km/h east. [2 marks] b. 12 N on a bearing of 25 and 17 N on a bearing of 100. [4 marks] 6. Determine the vertical and horizontal components of each vector. [6 marks] a. 810 N at an incline of 15 from horizontal b. 80 m/s, 60 clockwise from vertical 7. Given a = [2, -10] and b = [-8, 23], find: a. 3a - 2b [2 marks]7/31/23, 2:31 AM Vectors Assignment b. a . b [1 marks] c. a + b [2 marks] d. proj a [3 marks] e. The angle between a and b [2 marks] 8. Given p = [-1, 4, -8] and q = [10, 10, -9], find: a. 2p + 5q [2 marks] b. p . q [2 marks] c. q X p [3 marks] d. p x q [1 marks] e. The angle between p and q [3 marks] f. proj p [3 marks] 9. If u has a magnitude of 22 and v has a magnitude of 13, and the angle between them is 710, find the dot product of u and v. [2 marks] 10. Find the volume of the parallelepiped defined by the vectors u = [8, -3, 4], v = [-2, 9, 1], and w = [0, -1, 7]. [4 marks] 11. A force of [10,13] Newtons acts on an object as it moves along the displacement [8,-1] metres. Find the work done. [3 marks] 12. Given the points A(3, 5) and B(-3, -7) find: a. The vector equation of the line through them. [2 marks] b. The parametric equations of the line through them. [2 marks] c. The symmetric equation of the line. [2 marks] d. The scalar equation of the line. [2 marks] 13. Given the line [x, y, z] = [2, 6, -3] + t[4, 10, 5] find: a. The parametric equations of the line. [3 marks] b. The symmetric equation of the line. [3 marks]14. Find the vector and scalar equations for the plane through A(1, 0, 10), B(5, -5, 3), and C(8, 8, 2). [6 marks] 15. A pilot flies at 300 km/h with a heading of 110. A 30 km/h wind comes from 250. Find the bearing and speed of the plane's resultant travel. [5 marks] 16. Determine the values of k so that u = [3k, k + 10, -13] and v = [k - 5, -k, 1] are orthogonal. [3 marks] 17. Given the equations [x, y, z] = [7, -15, -4] + s[1, -2, 4] and [x, y, z] = [-15, -26, 23] + t[5, 1, -3], a. Identify whether the equations represent lines or planes. How do you know? [2 marks] b. Solve the system of equations to find the point of intersection. [5 marks] 18. Find the intersection of [x, y, z] = [1, 4, -2] + t[1, -1, 3] and 2x - 5y + 8z - 28 = 0. [4 marks] 19. Find the distance between the point (10, 100, 1000) and the plane [a, y, z = [1, 1, 1] + s [5, -5, 3] + t [-1, 1, 3]. [5 marks]