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Lecture 2-2 - Vectors components Numbersbreedvectors T h e...

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Vectors: components
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Numbers breed vectors We can also describe vectors using numbers. The vector connecting to is written as This uses the standard representation of vectors from before: force them to start at . The length of is A = (0, 0, 0) B = ( a , b , c ) v = æ a , b , c ç (0, 0, 0) v = æ a , b , c ç | v | = + + a 2 b 2 c 2 R
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Numbers breed vectors Any vector is made of three coordinates like that: Using this notation, the vector connecting the point to the point Note: you must always subtract the coordinates in the same order! A = ( a , b , c ) B = ( , , ) a b c = æ J a , J b , J c ç . AB ó a b c
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Brain massage Calculate the length of the vector connecting the point to the point . Consider the vectors and . Find such that Try this for another pair of vectors if you finish early. Rinse and repeat. (0, 2, 4) (1, J 1, 1) æ 1, 0, 0 ç æ 0, 1, 0 ç a , b , c æ 1, 0, 0 ç + æ 0, 1, 0 ç =
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