A pipeline is to be fitted under a road and can be represented on 3D Cartesian axes as below, with the -axis pointing East, the -axis North, and the -axis vertical. The pipeline is to consist of a straight section  directly under the road, and another straight section  connected to the first. All lengths are in metres. 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).   Write down a vector equation of the line BC . Hence find a and b .

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Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.