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mthsc206-fall-2010-notes-13.2

mthsc206-fall-2010-notes-13.2 - 13.2 Vectors Historic...

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13.2 Vectors Historic background: The first person to conceptualize force as a vector was Isaac Newton. Although Newton was able to conceptualize the idea of a vector, he provided no formal definition of what a vector was. William Rowan Hamilton, some 150 years after Principia , is given credit for the formal definition of a vector. Definition 13.2.1 A vector is an object that has a magnitude and a direction associated with it. Example 13.2.1 Give some examples of vectors. Definition 13.2.2 The vector with initial point A and terminal point B is called the displacement vector from A to B . Problem 13.2.1 What is the magnitude? What is the direction? Definition 13.2.3 Two vectors are equal or equivalent if they have the same magnitude and direction. Definition 13.2.4 The zero vector (denoted 0 or 0 ) is the vector with magnitude 0 and no specific direc- tion. We will see that there are two view points to take when talking about vectors: algebraic and geometric. We will discuss both, and use them interchangeably. Geometric Descriptions Vector addition: Given two vectors u and v , the vector sum u + v is the vector with the same magnitude and direction of the vector with the same initial point as u and terminal point as the vector v when it is positioned with the initial point of v coinciding with the terminal point of u .

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