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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
! ! 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.
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.
ex. From an old EF test: Vector A has a magnitude of 24.3 N, begins at the point (0,0) and

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

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