Chap12_Sec3

# Chap12_Sec3 - VECTORS AND THE GEOMETRY OF SPACE 12.3 The...

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12.3 The Dot Product VECTORS AND THE GEOMETRY OF SPACE In this section, we will learn about: Various concepts related to the dot product and its applications.

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If a = a 1 , a 2 , a 3 and b = b 1 , b 2 , b 3 , then the dot product of a and b is the number a • b given by: a • b = a 1 b 1 + a 2 b 2 + a 3 b 3 The result is not a vector. It is a real number, that is, a scalar. s For this reason, the dot product is sometimes called the scalar product (or inner product). THE DOT PRODUCT If a , b , and c are vectors in V 3 and c is a scalar, then PROPERTIES OF DOT PRODUCT 2 1. =| | 2. 3. ( ) 4. ( ) ( ) ( ) 5. 0 0 c c c = + = ⋅ + ⋅ = = ⋅ ⋅ = a a a a b b a a b c a b a c a b a b a b a
The dot product a • b can be given a geometric interpretation in terms of the angle θ between a and b. s This is defined to be the angle between the representations of a and b that start at the origin, where 0 θ π . In other words,

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## This note was uploaded on 02/23/2010 for the course MATH 221 taught by Professor Staff during the Spring '08 term at Tulane.

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Chap12_Sec3 - VECTORS AND THE GEOMETRY OF SPACE 12.3 The...

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