Vectors are used whenever there is a measurement in which not only the magnitude is relevant, but also the direction. Typical uses of vectors include position, velocity, acceleration, force, torque, and others.
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The Resultant Vector minus the other vector
We get the Unit Vector
If they are parallel, you can add them algebraically to get a resultant vector. Then you can resolve the resultant vector to obtain the vector components.
The normal vector to the surface is a radius at the point of interest.
R3 is a complete vector room, so you can actually take *ANY* other vector, e.g. from r1, r2 or r4 or any other vector room.