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Unformatted text preview: 1 Review: Vector Analysis REFERENCES: Arya Chapter 5. 1.1 Vectors A scalar has only a magnitude. A vector has both a magnitude and a direction. In this course, vectors will be represented in two ways (bold, or overarrow): R =- R, (1) or in the special case of a unit vector, with a hat (e.g. i ). The magnitude of a vector is represented R = | R | = |- R | (2) Vectors can be written in components. For example, in two dimensions: R = ( R x , R y ) (3) and R x = R cos( ) R y = R sin( ) (4) where R = R 2 x + R 2 y tan = R y R x (5) We also denote vectors with unit vectors : For example in 3D cartesian coordinates: i = (1 , , 0) , j = (0 , 1 , 0) , k = (0 , , 1) (6) where i is the unit vector associated with the x-axis direction, j the y-axis direction, and k the z-axis direction. Each has unit magnitute | i | = | j | = | k | = 1 (7) A general vector in 3D can then be represented as: R = ( R x , R y , R z ) = R x i + R y j + R z k (8) Adding and subtracting vectors can be done component-wise. From this, certain proper-Adding and subtracting vectors can be done component-wise....
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This note was uploaded on 09/20/2010 for the course AMATH 261 taught by Professor Rogermelko during the Spring '10 term at Waterloo.
- Spring '10