63_Multiplication_of_a_Vector_by_a_Scalar

63_Multiplication_of_a_Vector_by_a_Scalar - Calculus and...

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Calculus and Vectors – How to get an A+ 6.3 Multiplication of a Vector by a Scalar ©2010 Iulia & Teodoru Gugoiu - Page 1 of 2 6.3 Multiplication of a Vector by a Scalar A Multiplication of a Vector by a Scalar By multiplying a vector v r by a scalar k we obtain a new vector noted v k r with the following properties: a) v k r has the same direction as v r if 0 > k and the opposite direction if 0 < k b) || || | | || || v k v k r r × = B Properties The following properties apply for multiplication of a vector by a scalar: b k a k b a k r r r v + = + ) ( a km a km a m k r r r = = ) ( ) ( a m a k a m k r r r + = + ) ( Ex 1. Given the vector v r , draw the following vectors: a) v r 2 b) v r 3 d) v r 2 1 e) v r 4 1 Solution to Ex 1. Ex 2. Given k j i a r r r r + = 3 2 , k j i b r r r r 2 + + = , write the following expressions in terms of the vectors i r , j r , and k r . a) b a r r + k j i k j i k j i k j i b a r r r r r r r r r r r r r r 3 2 ) 2 1 ( ) 1 3 ( ) 1 2 ( ) 2 ( ) 3
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63_Multiplication_of_a_Vector_by_a_Scalar - Calculus and...

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