Intro to vectors.pdf

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M - Mathematics
M 273
Adam Wilander

Introduction to Vectors 1/18/2014 Vector: Magnitude and a direction ||V||=magnitude, v= entire vector (either bolded v or draw arrow on top of it) Magnitude: A number representing the length of vector. A vector with magnitude one can be pointed in any direction. Formula:√𝑋 + 𝑌 (In 2 dimensions, add z if in 3) Translate: Move vector to different location without changing magnitude or direction. Vector space: Any space with vectors. Linear Combination: Sum. Scalar multiplication of 2 or more vectors. EX: <4,4> is a linear combination of <6,2> and <2,4>. 2 2 Unit Vector: ||v||=1 Formula: v/ √ + 𝑌 Normalizing: Turning any vector into a unit vector. Triangle Inequality: ||v+w||≀||v||+||w|| the sum of 2 vectors is shorter than the 2 components individually.
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