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Chapter_3

# Chapter_3 - Chapter 3 Vectors In Physics we have parameters...

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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 . Speed, distance, 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 A unit vector Addition and subtraction of vectors using vector 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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Example : a displacement vector from position A to B. It 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 indicates the displacement direction . A vector can be shifted without changing its value if its length and direction are not changed. For example, the three arrows from A to B, from A' to B', and from A'' to B'', are equal to each other. Vectors are indicated in two ways: Method 1: (using an arrow above) Method 2: a (using bold face print) The magnitude of the vector is indicated by italic print: a a r (3-2)
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 r Negative of a given vecto Vector addition is has the same magnitude as but opposite directio r n + = + - - commutative b b b a b b a b b r r r r r r r r (3-3) = + s a b r a r b r a b + r r When is maximal? minimal? = + s a b r r r

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Geometric vector subtraction ( 29 ( 29 We write: From vector Then we add to vector We thus reduce vector subtraction to vector addition which we know how to do we find = = = - - + - - - d a d a b a b b b b b a r r r r r r r r r r r r Note: We can also add and subtract vectors using the method of components. For many applications the latter is a more convenient method (3-4) = - d a b r a r b r a b - r r b - r

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a+b=-c a+b=c a-b=c

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Reminders Register on wileyplus to do HW1 due by Jan 20 (next Wed) Buy and register iclicker to get ready for first quiz next Friday
2% tolerance!

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