Air Traffic Control

by Kimberly Black

Submitted : Spring 2014

In this investigation, I applied the knowledge acquired in my Calculus III course to evaluate the flight paths of the airplanes as vectors. I manipulated the vectors using concepts like the cross product of two vectors and the formula for the distance between a point in space and a plane in space. I found that the two lines did not intersect and were not parallel, but skew lines. It was also evaluated that the two lines were on parallel planes. I found the distance from one point on the first line to the second plane in order to figure out how far away the two aircrafts would be from each other.

Using the Java programming language, I created a program to calculate the above mathematical processes given any two lines in space. I tested it using the lines given for the problem to ensure its usability. After investigating these attributes of the two lines, I came to the conclusion that the two aircrafts’ flight paths would not intersect and were a good distance away from each other so there was no noticeable potential for conflict.

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