D2L 5.5 Assignment: Vectors - MCV4U X Vectors Assignment (No new emails) - maenshraim@ x ChatGPT X *Homework Help - Q&A from Onl x + O X 7 C A course.ilc.tvo.org//content/enforced/23228187-MCV4U-EN-02-03-ON-(1-D-0323)/course_content/assets/locker_docs/mcv4u_05.05.11.html?ou=23228187 G To on Update : 9. If u has a magnitude of 22 and u has a magnitude of 13, and the angle between them is 71, 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 [z, 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 [x, y, z] = [1, 1, 1] + s[5, -5, 3] + t [-1, 1, 3]. [5 marks] 1 25 C ENG 6:12 PM Mostly cloudy Q Search O (DELL W US 2023-08-02