15. Determine a value if t so that u = [9' t} and 1: :[_16' t] are perpendicular. [3 marks] _> 16. Determine if the vectors 7) : [53.1. '2]. h : ['.2..'1.1]undT> : [11.9. 4] are coplanar [6 marks] 17. Find the x, y and z intercept of the following plane 4x-82=16 [2 marks] \"of\" 9. Identify the type of triangle with vertices A(2,3,-5), B(-4,8, 1) and C(6,-4,0). [5 marks] 10. Determine the work done by the force F, in Newtons, for each object moving along. s [ 3 marks] F| = 2.5 260 IS | = 1.9 11. If i j and. T' are the standard basic vectors in 3-space, determine the value of K . (3 - 3 7 ) + ( 7 - 47) . (7- 472) -8 7x-7 (Simplify without using components). [3 marks] 9 of 11Part 2: Vectors (50 Marks Total) 7.A river is 2 000m wide and flows ay 6km/h. Marcus is driving a boat, which travels at 20km/h in still water. He sets out across the river perpendicular to the current. There is a marina directly across from his starting location. [5 marks] a. How far downstream from the marina will he end up? b. How long will it take him to get across the river in minutes? _p _. 8. Given u = (6,-1,5)and. V=(-3,-2,9) . a. A vector with a magnitude of 6, in the opposite direction 0 f. u in component form [3 marks] _, . b. The angle between. 11 and. V to the nearest degree [3 marks] 8234 PM Tue Jun 27 G} 80% - . Woo MCV4U Exam - 02-23 v \\ test practice x 8.3 MATH HW [Fa/QQCQQ E 12. Calculate the area of the parallelogram whose adjacent sides are l d = [-4, 5. '8]. b = [1: '2. 3] [4 marks] 13. Determine the parametric equation of the line whose direction vector is perpendicular to the direction vectors of the two lines 1 = 12 3 and. X_-5 = E = E and pass through the point (2,-5,0). [5 marks] *4 e7 3 3 2 4 14. Determine the following: 3. Determine the vector equation of the plane that contains the following two lines [ 4 marks] L1 = F(4, 3,5) + t(2,0, 3),t6R. L2 : FM, 3, 5) + 3(5, 1, 1),35R c. Determine the corresponding Cartesian equation. [3 marks]