lect10_1

# lect10_1 - Vectors In The Plane(10.1 1 Vectors A vector in...

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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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## This note was uploaded on 02/05/2012 for the course MATH 2142 taught by Professor Lerna during the Fall '10 term at FIU.

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lect10_1 - Vectors In The Plane(10.1 1 Vectors A vector in...

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