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Lecture+4+-+Ch.+3+st

Lecture+4+-+Ch.+3+st - Chapter 3 Vectors In physics we have...

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Chapter 3 Vectors In physics we have parameters that can be completely described by a number and are known as scalars . Temperature and mass are such parameters. Other physical parameters require additional information about direction and are known as vectors . Examples of vectors are displacement, velocity, and acceleration. In this chapter we learn the basic mathematical language to describe vectors. In particular we will learn the following: Geometric vector addition and subtraction Resolving a vector into its components The notion of a unit vector Addition and subtraction vectors by components Multiplication of a vector by a scalar The scalar (dot) product of two vectors The vector (cross) product of two vectors (3-1)

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Scalar - one dimensional quantity, that is, quantities which require only one number to giving its size or magnitude . Examples of scalar quantities are: Temperature Time Speed Mass Location Along a Line (1D) Vector - multi-dimensional quantity. Multi- dimensional quantities are those which require more than one number to completely describe them. Vectors, unlike scalars, have two characteristics, magnitude and direction . Examples of vector quantities are: Location in a Plane (2D) Location in Space (3D) Velocity Acceleration Force
An example of a vector is the displacement vector, which describes the change in position of an object as it moves from point A to point B . This is represented by an arrow that points from point A to point B . The length of the arrow is proportional to the displacement magnitude. The direction of the arrow indicated the displacement direction. The three arrows from A to B , from A' to B' , and from A'' to B'' , have the same magnitude and direction. A vector can be shifted without changing its value if its length and direction are not changed. In books vectors are written in two ways: Method 1: (using an arrow above) Method 2: a (using boldface print) The magnitude of the vector is indicated by italic print: a . a r (3-2)

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Geometric Vector Addition Sketch vector using an appropriate scale. Sketch vector using the same scale. Place the tail of at the tip of . The vector starts from the tail of and terminates at the tip of a b b a s a s a b = + r r r r r r r r r commutative: Negative of a gi .
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