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# notes001 (40) - 51 . The direction of v is u = 1 j v j v =...

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August 25, 2010 NAME____________________________ Let v be the vector v = h 5 ; 1 ; 5 i . In answering each of the following, you must show all of your work in order to get credit. (Just writing an answer is not su¢ cient.) a) Find the magnitude (length) of v . b) Find the direction of v . (In other words, ±nd the unit vector, u , that points in the same direction as v .) c) Find the vector, w , that has one half of the length of v and points in the same direction as v . d) Find the vector, r , that has length 4 and points in the opposite direc- tion of v . Solution: The magnitude of v is j v j = q 5 2 + ( 1) 2 + ( 5) 2 = p

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Unformatted text preview: 51 . The direction of v is u = 1 j v j v = 1 p 51 h 5 ; & 1 ; & 5 i = * 5 p 51 51 ; & p 51 51 ; & 5 p 51 51 + . The vector, w , that has one half of the length of v and points in the same direction as v is w = 1 2 v = 1 2 h 5 ; & 1 ; & 5 i = & 5 2 ; & 1 2 ; & 5 2 ± . The opposite of the direction of v is & u = * & 5 p 51 51 ; p 51 51 ; 5 p 51 51 + . 1 Thus the vector, r , that has length 4 and points in the opposite direction of v is r = 4 ( & u ) = 4 * & 5 p 51 51 ; p 51 51 ; 5 p 51 51 + = * & 20 p 51 51 ; 4 p 51 51 ; 20 p 51 51 + . 2...
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## This note was uploaded on 02/05/2012 for the course MATH 2203 taught by Professor Ellermeyer during the Fall '10 term at FIU.

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notes001 (40) - 51 . The direction of v is u = 1 j v j v =...

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