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12.2 Vectors

12.2 Vectors - Math 224 Calculus III 12.2 Vectors...

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Math 224 Calculus III 1 12.2 Vectors Recommended Homework: # 1-35(odds) Often quantities in science have both a magnitude and a direction associated with them: Example: Velocity Example: Force In order to handle this situation we describe these quantities using vectors : Picture & notation : Notes : To indicate a vector we write: v or v We can also indicate a vector by its start and end points: v AB The magnitude is represented by the length of the vector The magnitude (length) of the vector v AB is denoted v or AB or AB Two vectors are equivalent (or equal) if they have the same direction and the same magnitude. They DO NOT need to have the same position: v AB CD w The zero vector 0 is the vector with no length and no direction (or any direction!) A B v C D w

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Math 224 Calculus III 2 Vector Addition Consider the two vectors u and v : There are two ways (graphically) we can understand u+ v : Triangle Law Parallelogram Law Note that vector addition is commutative: u+v = v u Scalar Multiplication Multiplication of a vector by a constant (“scalar”) c The length of the vector c v
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