lect10_1

lect10_1 - Vectors In The Plane - (10.1) 1. Vectors A...

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Vectors In The Plane - (10.1) 1. Vectors A vector u ! in the plane is a directed line segment from an initial point P x 1 , y 1 to a terminal point Q x 2 , y 2 , denoted by " u 1 , u 2 # where u 1 $ x 2 ! x 1 and u 2 $ y 2 ! y 1 . The direction of u ! is PQ and the magnitude of u ! is the length of PQ defined by || u ! || $ u 1 2 % u 2 2 $ ! x 2 ! x 1 " 2 % ! y 2 ! y 1 " 2 (the distance between P and Q ). A vector is called a position vector the initial point is at the origin ! 0,0 " . Note that a vector in the plane is represented by a direction with a size. Elements u 1 and u 2 are called the first and second components of u ! . Example Find the vector with initial point at P ! 2,3 " and terminal point Q ! 3, ! 1 " and the vector with initial point at Q and the terminal point P . u ! $ PQ $" 3 ! 2, ! 1 ! 3 #$" 1, ! 4 # , v ! $ QP $" 2 ! 3,3 ! ! ! 1 " #$" ! 1,4 # 2. Vector Algebra Let u ! $" u 1 , u 2 # and v ! $" v 1 , v 2 # be vectors in the plane, and c is a constant. Then a. scalar multiplication:
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lect10_1 - Vectors In The Plane - (10.1) 1. Vectors A...

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