17 December 2011
Math is everywhere. No matter which way you look at it, it’s there. It is especially present in science. Most people don’t notice it, they have to look closer to find out what it is really made of. A component in math that is very prominent in science is the vector. What is a vector? A vector is a geometric object that has both a magnitude and a direction. A good example of a vector is wind. 30 MPH north. It has both magnitude,(in this case speed) and direction. Vectors have specific properties that make them very useful in real life applications. Through the use of these special objects, many advancements in the fields of math and science are available. Representations
Vectors can sometimes be hidden behind basic objects. They are usually represented with an arrow on top of its starting point and terminal point, as shown here: The most common form of vector is the bound vector. All that means is that the starting point of the vector is the origin, or (0,0). The bound vector goes from the origin to it’s terminal point, which in this case can be (3,4). An easy way to write this is A = (3,4), where A is the vector. On a graph, it looks like this:
That applies for two-dimensional vectors. Three dimensional vectors can be represented that way also. In a 3 dimensional vector, its terminal point has coordinates in three axis. These points can be represented by the letters i, j, and k. The letter i is for the x axis, j for the y axis, and k for the z axis. An example of a 3 dimensional vector is written as: A = 6i+3j+4k. It can also be denoted as A = (6,3,4). Where (6,3,4) is the terminal point. Two vectors are equal if their coordinates are equal, so if another vector, say B, had the terminal point (6,3,4), and if both vectors are bound vectors, they would be equal. Aside from direction, a vector has one other part, which is magnitude. Magnitude is denoted by the original vector...