I am learning vector analysis these days. I have some knowledge of the applications of the vector field in the field of Engineering and Astrophysics. I am also aware of the fact that vector field is a function that assigns a unique vector to each point in two or three dimensional space.(adsbygoogle = window.adsbygoogle || []).push({});

Firstly, What I donot understand is the need for vector-valued function. For example, we know that a position vector determines the position of a point in two or three dimensional space and the vector field or vector-valued function assigns this vector. Therefore why we use vector-valued function when the solution (value of x & y) of ordinary function can be represented graphically which also represents a unique point.

Secondly, I can fully imagine the graphical representation of a function in three dimensions (to some extent if the fourth dimension is time) but I cannot imagine a n variable function graphically. What is the logic behind these sort of functions and is it possible to graph these functions and if yes how?

Finally, I am learning about the vector-valued function of more than three dimensions therefore how the vector field assigns a unique vector to the points generated by these vectors (keeping in mind that we have only three units vectors namely i, j and k along x, y and z axes)?

Please answer these questions very comprehensively because I am very confused by these questions.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Preplexing Vector Fields

**Physics Forums | Science Articles, Homework Help, Discussion**