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Calculus Notes 13.2 - Calculus-Stewart Dr Berg Summer 09...

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Calculus- Stewart Dr. Berg Summer ‘09 Page 1 13.2 13.2 Vectors Interpretation of Vectors Vectors are commonly used to represent things that have magnitude and direction. Motion of an object has magnitude (distance) and direction. Force has magnitude (strength) and direction. We tend to think of vectors as arrows whose length is proportional to the magnitude. The two principle operations with vectors are vector addition and scalar multiplication . We model vector addition representing the sum of two vectors as the result of connecting the terminal point of one to the initial point of the other and taking the arrow having the initial point of the first and the terminal point of the second. Scalar multiplication produces a vector whose change in length is the magnitude (absolute value) of the scalar and in the same direction if positive and the opposite if negative. Examples: Definition A vector space V is a nonempty set of objects called vectors together with the
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