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Inside this Book – A few things need to be noted about the zero vector. Our motivation for what a vector is included the notions of magnitude and direction. What is the magnitude of the zero vector? We define it to be zero, i.e. k 0 k= 0. This agrees with the definition of the zero vector as just a point, which has zero length. What about the direction of the zero vector? A single point really has no well-defined direction. Notice that we were careful to only define the direction of a nonzero vector, which is well-defined since the initial and terminal points are distinct. Not everyone agrees on the direction of the zero vector. Some contend that the zero vector has arbitrary direction (i.e. can take any direction), some say that it has indeterminate direction (i.e. the direction can not be determined), while others say that it has no direction. Our definition of the zero vector, however, does not require it to have a direction, and we will leave it at that. 2 Now that we know what a vector is, we need a way of determining when two vectors are equal. This leads us to the following definition.
Inside this book –Vector Calculus PDF Book by Michael Corral – The point-vector correspondence provides an easy way to check if two vectors are equal, without having to determine their magnitude and direction. Similar to seeing if two points are the same, you are now seeing if the terminal points of vectors starting at the origin are the same. For each vector, find the (unique!) vector it equals whose initial point is the origin. Then compare the coordinates of the terminal points of these “new” vectors: if those coordinates are the same, then the original vectors are equal. To get the “new” vectors starting at the origin, you translate each vector to start at the origin by subtracting the coordinates of the original initial point from the original terminal point. The resulting point will be the terminal point of the “new” vector whose initial point is the origin. Do this for each original vector then compare.
Vector Calculus by Michael Corral PDF : eBook Information
- Full Book Name – Vector Calculus
- Author of this Book – Michael Corral
- Language – English
- Book Genre – Novel, Calculus, Multivariable, Mathematics, Vector Analysis
- Download Format – PDF
- Size – 2.4 MB
- eBook Pages –222
- Price – Free