Part 4 A pipeline is to be fitted under a road and 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...

Extracted text: Part 4 A pipeline is to be fitted under a road and 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. Y (N) C(a, b, 0) A (0, -40, 0) X (E) B (40, 0, -20) (a) Calculate the distance AB. The section BC is to be drilled in the direction of the vector 3ị + 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.