You are expected to demonstrate vector techniques from Topic 1. Using alternative methods will result in low or no marks. 1. (a) Show that the vectors v = i + 3j + 5k and w = 2i 4j + 2k are perpendicular. (b) Resolve the vector v = 2i3j+2k into two vectors, one parallel to w = 2i+j+2k and one perpendicular to w = 2i + j + 2k. (c) Find the intersection of the lines, L1 : (x, y, z) = (1, 3, 1) + t(3, 1, 2) and L2 : (x, y, z) = (2, 0, 1)) + t(1, 2, 1). (d) Determine the equation of the plane that passes through the point P = (1, 2, 1) and is perpendicular to the line L : x3 6 = y+1 2 = z 2. (e) Find the area of the triangle with vertices at the points A(1, 1, 1), B(3, 0, 4) and C(2,1, 4).