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66_Operations_with_Algebraic_Vectors_in_R2

66_Operations_with_Algebraic_Vectors_in_R2 - Calculus and...

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Calculus and Vectors – How to get an A+ 6.6 Operations with Algebraic Vectors in R 2 ©2010 Iulia & Teodoru Gugoiu - Page 1 of 2 6.6 Operations with Algebraic Vectors in R 2 A 2D Algebraic Vectors A 2D Algebraic Vector may be written in components form as: ) , ( y x v v v = r or in terms of unit vectors as: j v i v v y x r r r + = and has a magnitude given by: 2 2 || || y x v v v + = r Ex 1. Consider the vector j i a r r r 4 3 + = . a) Write the vector in components form. ) 4 , 3 ( 4 3 = + = j i a r r r b) Find the magnitude of the vector a r . 5 25 4 ) 3 ( || || 2 2 2 2 = = + = + = y x a a a r B Addition of 2D Algebraic Vectors The sum of two 2D algebraic vectors j a i a a a a y x y x r r r + = = ) , ( and j b i b b b b y x y x r r r + = = ) , ( is a 2D algebraic vector given by: ) , ( ) ( ) ( y y x x y y x x y x y x b a b a j b a i b a j b i b j a i a b a + + = + + + = + + + = + r r r r r r r r Ex 2. Find the sum of the vector j i a r r r 5 3 = and ) 7 , 2 ( = b r . j i b a s r r r r r 2 ) 2 , 1 ( ) 7 5 , 2 3 ( + = = + = + = C Subtraction of 2D Algebraic Vectors The difference of two 2D algebraic vectors j a i a a a a y x y x r r r
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