1. Determine the coordinates of the point of intersection of the line 'l' defined by the parametric equations and the plane ? defined by the scalar equation. (6 marks) I : x = 4 + t y = 2 -2t z = 6 + 3t? : x + 5y +z - 8 = 0Q.41. An airplane is flying at an airspeed of 550 km/h, on a heading of 080. A 60-km/h wind is blowing from a bearing of 120. Determine the ground velocity of the airplane and the direction of flight. 3. A wrench is used to tighten a bolt. A force of 90 N is applied in a counter clockwise direction at 70 to the handle, 15 cm from the centre of the bolt.a) Calculate the magnitude of the torque.b) In which direction does the bolt move?

2. Determine the value of k so that u = [4 ,1, 3] and v = [-1 ,5, k] are orthogonal. 3. The initial point of vector MN = [2 , 4 ,-7] is M(-5 ,0 ,3). Determine the coordinates of the terminal point , N. 4. the area of the parallelogram defined by the vectors u = [6 ,3, 8] and v = [3, 3, 5]. Determine the angle between vectors u and v Que.3 Do the following sums.(C) (18 marks) 1. what is the magnitude of 4 for any vector ? (2 marks) 2. Explain what the term consistent means in the context of a system of three planes. 3. Explain how the vectors ,5 7 , and -5 7 are related. (3 marks) 4. Is the following statement true or false ? Explain your decision. " if u x v=v x u, then u is orthogonal & v. 5. Prove distributive property of vectors addition using 2 -D Cartesian vectors. 6. Write some application of the dot product measure? 4.2. The plane it has vector equation = [2,1,3] + s[1,1,1] + t[2,0,2] , s,t ER. a. Verify that i does not pass through the origin. b. Find the distance from the origin to n