A cable is to be installed under a road and its route can be represented on 3D Cartesian axes as below, with the x-axis pointing East, the y-axis North, and the z-axis vertical. The pipeline is to consist of a straight section AB directly under the road, and another straight section BC connected to the first. All lengths are in metres. A (0, -40, 0) | X (N) C (a, b, 0) B (40, 0, -20) x (E) a. Calculate the distance AB. The section BC is to be drilled in the direction of the vector 3i+4j + k. b. Find the angle between the sections AB and BC. The section of pipe reaches ground level at the point C (a, b, 0). C. Write down a vector equation of the line BC. Hence find a and b.