Lec3-DotProduct

# Lec3-DotProduct - The Dot Product Math 32 A Lecture for...

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The Dot Product Math 32 A Lecture for Friday, October 2 Professor: Jon Rogawski

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The Dot Product
The Dot Product Definition of the Dot Product

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The Dot Product Definition of the Dot Product Geometric Interpretation
The Dot Product Definition of the Dot Product Geometric Interpretation Projection and Component of a vector u along a vector v

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Definition of Dot Product v . w Given two vectors: v = < a 1 , b 1 , c 1 > w = < a 2 , b 2 , c 2 >
Definition of Dot Product Given two vectors: v = < a 1 , b 1 , c 1 > w = < a 2 , b 2 , c 2 > v . w = a 1 a 2 + b 1 b 2 + c 1 c 2

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Definition of Dot Product v = < a 1 , b 1 , c 1 > w = < a 2 , b 2 , c 2 > Multiply Components and Add v . w = a 1 a 2 + b 1 b 2 + c 1 c 2
Let s compute the dot product v = < 2 , -4 , 5 > w = < 3 , 2 , -5 >

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Let s compute the dot product v = < 2 , -4 , 5 > w = < 3 , 2 , -5 > v . w = (2)(3) + (-4)(2) + (5)(-5) = 6 - 8 - 25 = - 27
Dot Product In 2 - D v = < 4 , 3 > w = < 1, -5 > v . w = (4)(1) + (3)(-5) = 4 - 15 = -11

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Basic Properties of Dot Product
Basic Properties of Dot Product 0 . v = v . 0 = 0 ( 0 is the zero vector)

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Basic Properties of Dot Product 0 .
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## This note was uploaded on 02/13/2010 for the course MATH MATH 32A taught by Professor Park during the Fall '09 term at UCLA.

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Lec3-DotProduct - The Dot Product Math 32 A Lecture for...

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