64_Properties_of_Vectors

# 64_Properties_of_Vectors - Calculus and Vectors How to get...

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Calculus and Vectors – How to get an A+ 6.4 Properties of Vectors ©2010 Iulia & Teodoru Gugoiu - Page 1 of 2 6.4 Properties of Vectors A Properties of Vectors a b b a r r r r + = + a a a r r r r r = + = + 0 0 0 ) ( ) ( r r r r r = + = + a a a a ) ( ) ( c b a c b a r r r r r r + + = + + || || | | || || a k a k r r = b k a k b a k r r r r + = + ) ( ) ( ) ( ) ( a k l a l k a kl r r r = = a l a k a l k r r r + = + ) ( a a r r = 1 a a r r = ) 1 ( 0 0 r r = a 0 || 0 || = r Ex 1. If j i a r r r 3 2 = and j i b r r r + = , find i r and j r in terms of a r and b r . j i a r r r 3 2 = (1) j i b r r r + = (2) From (2): i b j r r r = (3) Let substitute (3) into (1): 5 3 5 3 ) ( 3 2 b a i i b a i b i a r r r r r r r r r r + = = + = (4) Let substitute (4) into (3): 5 2 5 3 5 5 3 a b b a b b a b j r r r r r r r r r = = + = 5 2 , 5 3 b a j b a i r r r r r r + = + = Ex 2. Consider the triangle ABC . Let M be the midpoint of AC and N

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64_Properties_of_Vectors - Calculus and Vectors How to get...

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