# Math Vectors Essay

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

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The magnitude is useful in many aspects of vectors, such as the dot product or the cross product. I will explain the two soon.

Dot Product One very important operation that is useful for working with vectors it the dot product. The dot product of a vector is the vector squared, if you are only using one vector. If two vectors are being used, the equation is: . In words, this is the magnitude of one vector times the magnitude of the other times the cosine of the angle between them. Another way of getting the dot product is multiplying each pairing term of one vector with the other and then adding them. The answer will be a number, unlike the cross product, which comes out to be another vector. Below is an example with the vectors: a = (4,3,5), b = (1,3,2):

The dot product is useful if you need to find the angle between the two vectors. Since the equation is: , the cosine function can be left alone, making the equation for the angle: . Below is an example of finding the angle between the same two vectors from above:

Cross Product Another useful operation when working