preview

Math Vectors

Decent Essays

MIchael Driesen Mrs. Rozell Math 10H 17 December 2011 Vectors 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 …show more content…

The equation for the cross product is: . It can also be written as: The easiest way of finding the cross product is by setting the coordinates up in a 3x3 matrix. A matrix is a way of organizing data. Using i, j, and k as place holders and using the same two vectors from before, the matrix would look like this: Now, in order to get the new vector, the determinant has to be found. The work for the determinant is below: The final vector is a vector that is orthogonal to the other two. This is a good representation of what it would look like: The cross product is necessary to find the amount of torque or work needed or used. Other Vectors Null Vector: The null vector is a vector that has the length (magnitude) of 0. It is written as (0,0,0) and if c is a null vector and a is a normal one, c+a=a. Unit Vector: This vector is more about direction than magnitude. The unit vector has a magnitude of one, always. Turning a vector into its unit vector is easy. Just divide the vector by its magnitude. This is called the normalization of a vector. Adding Vectors Adding vectors is very easy. All that is needed is a knowledge of trigonometry. Specifically, the law of cosines and the law of sines. To add two vectors, simply stick them head to tail, and

Get Access