Part A: Knowledge (16 marks) 1. Let L, be the line with vector equation r = (-2,3) + s(-1,3), s E R. Let L2 be the line with parametric equations x = 3t + 2, y = t - 7, t E R. Are the two lines perpendicular? Justify your answer using proper terminology. [4 marks] 2. Determine the Cartesian equation of the line with parametric equations x = 2t - 1, y = 4t + 2, t E R. [4 marks] 3. At what point does the line L1: (10,7,5) + s(-4, -3,2), s E R intersect the plane T1: 6x + 7y + 10z - 9 = 0? [4 marks] 4. What is the direction vector for the line of intersection between the planes m, : 3x - y + 2z = 100 and 12: x + 3y = 45? [4 marks] Part B: Application (18 marks) 5. Determine the vector equation of a line passing through the point P(3,2, -1) and with a direction vector perpendicular to the line r = (2, -3,4) + s(1,1, -2), s E R. [3 marks] 6. Determine the Cartesian form of the plane whose equation in vector form is T = (-2,2,5) + s(2, -3,1) + t(-1,4,2), s, t E R. [4 marks] 7. Determine the Cartesian equation of the plane that contains the line T = (0.3.4) + s(2.2,1), s E R and the point P(2,1,0). [3 marks]