5_Vectors_(notes)

5_Vectors_(notes) - Vectors 3D Coordinate System Graph P(2,...

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Vectors 3D Coordinate System Graph P(2, 4, -2) and Q(-3, 0, 5)
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A vector is a quantity specified by magnitude and direction. A scalar is a quantity specified by magnitude only. Geometric Vectors are represented by an arrow. Operations ! u + ! v
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! ! u ! u ! " v 2 ! u ! ! u + 3 ! v
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**** Two vectors are parallel if they are scalar multiples of each other.***** ! u ! v ! ! u = c " v , c is a nonzero constant. If c > 0, the vectors go in the same direction. If c < 0, the vectors go in the opposite direction. i is the unit vector in the positive x direction. j is the unit vector in the positive y direction.
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PQ = q 1 ! p 1 ( ) i + q 2 ! p 2 ( ) j = q 1 ! p 1 , q 2 ! p 2 ex. The magnitude of v, ! v or ! v = v 1 2 + v 2 2 . A unit vector is a vector of length 1. u = v v
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A vector is a product of magnitude and direction. v ! = v ! v ! v ! " # $ $ % & Direction is a UNIT vector. Algebraic addition: ex. Find the horizontal and vertical components of v if v has magnitude 3 and makes an angle of 20 degrees with the horizontal.
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ex. From an old EF test:
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This note was uploaded on 03/29/2008 for the course MATH 1224 taught by Professor Dontremember during the Spring '08 term at Virginia Tech.

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5_Vectors_(notes) - Vectors 3D Coordinate System Graph P(2,...

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