Lec1-Vectors

# Lec1-Vectors - Componentwise Addition Linear Combinations...

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Math 32A Multivariable Calculus Professor Jon Rogawski

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LECTURE 1: VECTORS
Basics of Vectors Definitions Addition and Scalar Multiplication Unit Vectors Vectors in R 3 Parametric Equations of a Line

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DEFINITION v y z A vector is an arrow in the plane R 2 or in 3-space R 3 x
Vectors indicate MAGNITUDE and DIRECTION z y x

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HEAD AND TAIL (INITIAL AND TERMINAL POINT)

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LABELING VECTORS v = P 1 Q 1 w = P 2 Q 2
Equivalent Vectors

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Components
Scalar Multiplication

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Vector Addition v w v + w Parallelogram Law

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Unformatted text preview: Componentwise Addition Linear Combinations Unit Vectors Basic Unit Vectors: i , j Basic Unit Vectors: i , j RIGHT-HANDED SYSTEM RIGHT-HANDED SYSTEM LEFT-HANDED SYSTEM Coordinates in R 3 Vector in R 3 Translation in R 3 Parallelogram Law in R 3 Basic Unit Vectors: i, j, k Lines in R 3 Lines in R 3 Vector Multiplication v w Dot Product v . w (a number, not a vector) Cross Product v x w (non-commutative!)...
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Lec1-Vectors - Componentwise Addition Linear Combinations...

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