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67_Operations_with_Algebraic_Vectors_in_R3

# 67_Operations_with_Algebraic_Vectors_in_R3 - Calculus and...

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Calculus and Vectors – How to get an A+ 6.7 Operations with Algebraic Vectors in R 3 ©2010 Iulia & Teodoru Gugoiu - Page 1 of 3 6.7 Operations with Algebraic Vectors in R 3 A 3D Algebraic Vectors A 3D Algebraic Vector may be written in components form as: ) , , ( z y x v v v v = r or in terms of unit vectors as: k v j v i v v z y x r r r r + + = and has a magnitude given by: 2 2 2 || || z y x v v v v + + = r Ex 1. Consider the vector k j i a r r r r 2 3 + = . a) Write the vector in components form. ) 2 , 3 , 1 ( 2 3 = + = k j i a r r r r b) Find the magnitude of the vector a r . 14 ) 2 ( 3 ) 1 ( || || 2 2 2 2 2 2 = + + = + + = z y x a a a a r B Addition of 3D Algebraic Vectors The sum of two 3D algebraic vectors k a j a i a a a a a z y x z y x r r r r + + = = ) , , ( and k b j b i b b b b b z y x z y x r r r r + + = = ) , , ( is a 3D algebraic vector given by: k b a j b a i b a k b j b i b k a j a i a b a z z y y x x z y x z y x r r r r r r r r r r r ) ( ) ( ) ( ) ( ) ( + + + + + = + + + + + = + ) , , ( ) , , ( ) , , ( z z y y x x z y x z y x b a b a b a b b b a a a b a + + + = + = + r r Ex 2. Find the sum of the vector k j i a r r r r + = 5 2 and ) 3 , 0 , 2 ( = b r . k j b a s r r r r r 4 5 ) 4 , 5 , 0 ( ) 3 1 , 0 5 , 2 2 ( ) 3 , 0 , 2 ( ) 1 , 5 , 2 ( = = + + = + = + = C Subtraction of 3D Algebraic Vectors The difference of two 3D algebraic vectors k a j a i a a a a a z y x z y x r r r r + + = = ) , , ( and k b j b i b b b b b z y x z y x r r r r + + = = ) , , ( is a 3D algebraic vector given by: k b a j b a i b a k b j b i b k a j a i a b a z z y y

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67_Operations_with_Algebraic_Vectors_in_R3 - Calculus and...

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