(Solved): M4-2/D4-2. A pipeline is to be fitted under a road and can be represented on 3D Cartesian axes as b ...

M4-2/D4-2. 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 \( A B \) directly under the road, and another straight section \( B C \) connected to the first. All lengths are in metres. i. Calculate the distance \( A B \). ii. The section \( B C \) is to be drilled in the direction of the vector \( 3 \boldsymbol{i}+4 \boldsymbol{j}+\boldsymbol{k} \). iii. Find the angle between the sections \( A B \) and \( B C \).