y(N) C(a, b, 0) A (0, -40, 0), x (Е) B (40, 0, -20) 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...

Task 2

Scenario

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 straight section BC connected to the first. All lengths are in metres.

Extracted text: y(N) C(a, b, 0) A (0, -40, 0), x (Е) B (40, 0, -20) 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.