MATH 125 Lecture Notes - Lecture 14: Parallelogram, Pythagorean Theorem
29 Sep 2015
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Math 125 - lecture 14 - introduction to vectors. Sometimes you need one object to hold multiple pieces of information. Example: the weather channel wants to post censors around a grid in urbana. You must gather two pieces of information. Each point on the grid stores two pieces of information. It is an ordered n-tuple of numbers. This contains information on magnitude and direction. You can graph what direction the vector pushes you in. The length of the vector is how far you"ve traveled in that direction (magnitude) Use pythagorean theorem to find the value of the vector. The wind speed at this point is 10. Example: suppose the weather station maps urbana on a 3d grid. This vector only gives two pieces of information. We can think of nx1 matrices as vectors. Define operations in a way that preserves their meaning. U+v = moved by u, then moved by v. U+v= <5,7> = <2+3, 3+4> = <2,3> + <3,4>
